Clay RSS Feed - Statistics

A Theory of the Mechanics of Information: Generalization Through Measurement of Uncertainty (Learning is Measuring)

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2510.22809v2 Announce Type: replace-cross Abstract: Traditional machine learning relies on explicit models and domain assumptions, often limiting flexibility and interpretability. We introduce a "model-free" framework of instance-based learning using surprisal (information theoretic uncertainty) to directly analyze and perform inferences from raw data, eliminating distribution modeling, reducing bias, and enabling efficient updates including direct edits and deletion of training data. By quantifying relevance through uncertainty, the approach enables generalizable inference across tasks including generative inference, causal discovery, anomaly detection, and time series forecasting. Our approach emphasizes traceability, interpretability, and data-driven decision making, offering a unified, human-understandable framework for machine learning, can be adapted to virtually all machine learning tasks, achieving competency across all and state-of-the-art performance on anomaly detection and some supervised tasks. The mathematical foundations create a "physics" of information, which enable these techniques to apply effectively to a wide variety of complex data types, including missing data. Our results suggest that this may be a viable foundation upon which to build scalable machine learning and artificial intelligence that can maintain human understandability of the underlying mechanics.

Minimax Rates for Learning Smooth Populations of Parameters

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.04135v2 Announce Type: replace Abstract: We study pointwise estimation of a smooth binomial mixing density and characterize its minimax rates. Assuming that the mixing density is $s$-H\"older smooth, we first consider the homogeneous setting with a common number of binomial trials $t$. We derive matching lower and upper bounds that reveal three regimes depending on the relative sizes of the sample size $n$ and the number of trials $t$. When $t$ is small, the finite number of trials creates an identification barrier that persists regardless of sample size; at intermediate $t$, more data reduce sampling uncertainty, while the number of trials limits how finely the mixing density can be recovered; and when $t$ is sufficiently large, the usual nonparametric density estimation rate is recovered. Our lower bounds exploit the polynomial structure of the binomial mixture model, while attainability is achieved by a suitably regularized orthogonal series estimator. We then extend the analysis to heterogeneous trial parameters, where the minimax rate depends on the full trial profile through the effective sample size available at each polynomial degree. These results characterize the fundamental statistical limits of learning smooth populations of binomial probabilities under both homogeneous and heterogeneous trials.

Posterior Consistency for Recovering Initial States in Nonlinear Subdiffusion Equations

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2608.26536v3 Announce Type: replace Abstract: We study the Bayesian recovery of the initial state in a semilinear time-fractional subdiffusion equation from noisy random space-time point observations. A rescaled Gaussian prior based on a Whittle--Mat\'ern process is assigned to the unknown initial condition. We prove that the solution has $\dot H^3$-regularity when the nonlinearity satisfies a Lipschitz condition in the Sobolev norm. We then establish posterior contraction rates for the prediction error in the $L^2$-norm and for the parameter in Sobolev norms. The rates are polynomial in the sample size, with exponent depending on the prior smoothness and the spatial dimension. Moreover, we prove a minimax lower bound by constructing a wavelet-packing set and controlling the Kullback--Leibler divergences.

How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2607.14812v4 Announce Type: replace Abstract: We study the worst-case false discovery rate (FDR) of the Benjamini-Hochberg procedure for both one- and two-sided Gaussian tests with general correlation matrices. For each setting and given target FDR level $q$, we construct a family of finite Gaussian models whose FDR divided by $q$ diverges as $q\downarrow0$. This disproves any universal multiplicative FDR bound. Moreover, we establish new FDR lower bounds that are independent of the number of hypotheses. For two-sided tests, the worst-case FDR over the number of hypotheses, mean vector, and correlation matrix is at least an explicit ${\ell_{=}}(q)>q$: \[ \ell_{=}(q)=\frac{q\sqrt{\log(1/q)}}{2\sqrt{\pi}}+c_\ell q+o(q), \qquad c_\ell=0.6492828\ldots. \] For one-sided tests, we show a lower bound $\ell_{\le}(q)>q$: \[ \ell_{\le}(q)=\frac{q\sqrt{\log(1/q)}}{\sqrt\pi} +\frac q2+o(q). \] Finally, we prove the leading constants are sharp for a class of correlation matrices for both one- and two-sided tests.

Dense alternating sign matrices and imprecise copulas

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2607.06178v2 Announce Type: replace Abstract: In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We identify dense alternating sign matrices as a particularly well-behaved subclass. We prove that the associated discrete imprecise copulas are always coherent and hence avoid sure loss. We further show that a particular extension of the corresponding discrete quasi-copulas to the full domain preserves this structure and yields self-dual imprecise copulas. To the best of our knowledge, this provides the first general result in the literature showing how properties established for discrete imprecise copulas can be preserved when extending them to their full-domain counterpart. We conclude the paper by showing that, for general alternating sign matrices, the associated discrete imprecise copulas need not avoid sure loss, further emphasizing the special role of the subclass of dense alternating sign matrices. We establish, however, that the class of discrete quasi-copulas of minimal range is invariant under all defect transformations

The Harmonic Entropy Estimator: Minimax Optimality and Semiparametric Efficiency for Infinite Alphabets

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2505.20153v5 Announce Type: replace Abstract: Shannon entropy estimation for discrete distributions is a classical nonparametric problem whose statistical limits are well characterized under finite support. Whether minimax and efficiency guarantees extend to infinite-support distributions remains open, in part because the expectation and variance of logarithm-transformed multinomial counts lack closed forms, forcing analyses to rely on bounding arguments rather than exact moment expressions. We address this obstacle with an algebraic framework built on an exact identity relating harmonic-transformed counts to their log-probabilities, yielding the harmonic entropy estimator. With this framework, we obtain two main results characterizing the statistical limits of this problem for distributions with sufficiently fast-decaying tails. First, for the class of distributions with at least quadratically decaying tails ($p_j \lesssim j^{-2}$), we establish that the $L_2$-minimax convergence rate is $1/n$, a rate anchored by estimator variance for both finite- and infinite-support distributions. Second, under the stronger condition $p_j = o(j^{-2})$, we demonstrate that the harmonic estimator is semiparametrically efficient: $\sqrt{n}[\hat{H}(\mathbf{X}_n) - H(X)]$ converges weakly to a normal distribution with variance achieving the semiparametric efficiency bound, $\mathrm{Var}[\log p(X)]$. Furthermore, the harmonic estimator is universally less biased than the plug-in estimator by circumventing the approximation error inherent to expectations of logarithm-transformed counts. More broadly, the harmonic approach may provide a foundation for developing new theory in entropy-based estimation, such as inference for mutual information under similar nonparametric regimes.

Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13442v1 Announce Type: cross Abstract: Compression schemes provide a general framework for deriving data-dependent risk bounds for learning algorithms. For learning rules based on preferent compression, existing results upper-bound the risk in terms of a sample-dependent complexity $\boldsymbol{k}$, defined as the cardinality of the compression augmented by the training examples on which the reconstructed hypothesis is inappropriate. These results, however, yield a margin of order $O(\sqrt{\ln N/N})$ above $\boldsymbol{k}/N$. In this paper, we establish that the logarithmic factor is not intrinsic. We prove that, for every fixed confidence level $1-\delta$, the risk is bounded with probability at least $1-\delta$ by $$ \frac{\boldsymbol{k}}{N} + O\left(\frac{1}{\sqrt{N}}\right), $$ uniformly over all possible values of $\boldsymbol{k}$. Thus, risk estimates for learning algorithms based on preferent compression attain the same law-of-large-numbers rate as the empirical estimate of the probability of a fixed event. We also show that the leading term $\boldsymbol{k}/N$ is necessary and investigate its relation to the empirical risk. In particular, we identify regimes in which the empirical risk retains the $O(1/\sqrt{N})$ convergence rate, as well as regimes in which it converges more slowly or ceases to be consistent, while the complexity-based estimator preserves the $O(1/\sqrt{N})$ rate.

The Order Mass Identity of Rooted Forests, with a Direct Proof of the Extended Aldous--Broder Theorem

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13063v1 Announce Type: cross Abstract: Random spanning forests provide probability models for partitions and Monte Carlo methods on graphs. In these applications, the distribution produced by a sampler determines which forest functionals can be estimated. The Aldous--Broder algorithm constructs a spanning tree from the first-entrance edges of a covering random walk. Its distribution is known, but a direct calculation requires summing over all orders in which a fixed tree can be discovered. We evaluate this sum through an identity for rooted forests and real matrices with zero row sums. Under a nonsingularity condition on the principal submatrices encountered during growth, the sum of products of harmonic extension entries equals a principal cofactor of a matrix on the roots. With one root, the sum is one. The identity gives a direct proof of the extended Aldous--Broder theorem for every finite irreducible Markov chain started at a fixed state, without assuming reversibility or bidirectional transition support. It also gives the conditional distribution of the discovery order and the law of the forest obtained by stopping after all nonroot vertices have been visited. A completion weight describes the difference between this stopped-walk law and the weight-proportional forest law, including the support restriction needed for importance correction. Numerical examples illustrate the sampling implications. The identity, the Aldous--Broder theorem, and the stopped-forest law are formalized in Lean4.

An efficient stochastic generalized method of moments estimator for nonlinear moment models

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12873v1 Announce Type: cross Abstract: We study the asymptotic properties of the nonlinear stochastic GMM algorithm proposed by Chen, Lee, Liao, Seo, Shin and Song for recursively estimating parameters defined by possibly nonlinear and overidentified moment restrictions $\E[g(X,\beta^*)]=0$. Each observation updates estimates of the moment Jacobian, inverse covariance matrix and Gauss--Newton preconditioner at a cost independent of sample size. For linear and nonlinear instrumental-variable moments, we derive an exact rank-two Sherman--Morrison--Woodbury update. The algorithm combines preconditioned stochastic approximation with iterate averaging. Under a preconditioned monotonicity condition, satisfied globally in linear models and locally around a consistent pilot estimate in general, we establish almost sure convergence and rates, as well as a functional central limit theorem with the efficient GMM variance. These results require four moments of the moment function and its Jacobian when the step exponent exceeds $2/3$. The inverse Gauss--Newton matrix consistently estimates this variance, and a projected linearised statistic enables online testing of overidentifying restrictions. We extend the results to $L$-dependent data with long-run variance weights under stronger moment assumptions. Simulations show that the averaged estimator approaches offline two-step GMM in accuracy and coverage at $10^6$ observations, while requiring a fraction of its computing time and fixed memory at up to $10^7$ observations. The online test achieves correct size and comparable power. In an application estimating the effect of a third child on weeks worked using $254{,}654$ women from the 1980 US Census, single-pass estimates agree with offline GMM within a fraction of a standard error on average across data orderings, and both methods yield the same overidentification-test conclusion in most orderings.

Effective-dimension bounds in the central limit theorem for centered Euclidean balls

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12722v1 Announce Type: cross Abstract: We establish a nonasymptotic Gaussian approximation bound over centered Euclidean balls for sums of independent, not necessarily identically distributed, random vectors in $\mathbb R^p$. Let $S_n$ denote the sum, let $\Sigma=\operatorname{Var}(S_n)$, and let $G\sim N(0,\Sigma)$. Define the effective rank and the normalized squared spectral mass by \[ r(\Sigma)=\frac{\operatorname{tr}\Sigma}{\|\Sigma\|}, \qquad v(\Sigma)=\frac{\operatorname{tr}(\Sigma^2)}{\|\Sigma\|^2}. \] Under a uniform directional fourth-moment condition, covariance-balance assumptions, and the spectral conditions $r(\Sigma)\le C_\Sigma v(\Sigma)$ and $v(\Sigma)\ge6$, we prove \[ \sup_{z\ge0} \left| \mathbb P\{\|S_n\|^2\le z\} - \mathbb P\{\|G\|^2\le z\} \right| \le C\,\frac{r(\Sigma)^{3/2}}{n}. \] The constant depends only on the fixed parameters in the assumptions and is independent of the ambient dimension and individual small eigenvalues of the covariance matrix. The bound is uniform at the endpoint $v(\Sigma)=6$, without a logarithmic loss. Its main feature is the combination of the $n^{-1}$ rate with dependence on effective rank, including this endpoint. Consequently, the bound can vanish when $r(\Sigma)=o(n^{2/3})$, even when $p$ is much larger than $n$. The same estimate extends to random elements of a separable Hilbert space with trace class covariance. The proof builds on the Fourier and symmetrization methods of \citet{GoetzeZaitsev2014}, combined with moment matching, truncation, and comparison estimates that retain the covariance structure.

Transformer-Based Masked Diffusion Models Provably Learn Distributions with Latent Structure

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12544v1 Announce Type: cross Abstract: Masked diffusion models (MDMs) generate discrete data by iteratively unmasking multiple tokens in parallel using a learned mask predictor. Their output carries two errors: parallelization error due to parallel sampling, and estimation error from the mask predictor learned with finite samples. Existing theory treats these errors separately, and the available statistical bounds typically scale with the number $V^L$ of length-$L$ sequences over a vocabulary of size $V$, suffering from the curse of dimensionality. In this work, we establish end-to-end statistical guarantees showing that transformer-based MDMs learn structured distributions with a sample complexity governed by their latent structure. Specifically, we model this structure through mixtures of hidden Markov trees, which capture latent dependencies within components and heterogeneity across components. When the data distribution is well approximated by such a mixture, a transformer-based MDM with parallel unmasking schedules achieves $\varepsilon$-accurate sampling in KL divergence with $\widetilde{O}(LK_{\mathrm{par}}/\varepsilon)$ training samples, where $K_{\mathrm{par}}$ is polynomial in $L$, $V$, the number of hidden states, and the number of mixture components. The transformer network and sampling procedure require no knowledge of the tree topologies or component parameters, thereby adapting to the unknown latent structure automatically. Overall, our results provide theoretical justification for the empirical effectiveness of MDMs on real-world data.

On diagonal sections of Markov products of copulas

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13846v1 Announce Type: new Abstract: Given a bivariate copula $C$, the bivariate copula $\Psi(C)$ is defined as the Markov product of $C^T$ and $C$. In this paper we consider the diagonal section of $\Psi(C)$ under the additional assumption that its value at a single point is known. We determine the exact upper and lower bounds for the diagonal section of $\Psi(C)$, given that $\Psi(C)(a,a)=d \in [a^2,a]$, where $a \in [0,1]$ is a fixed point. Furthermore, we describe some additional properties of the transformation $\Psi$, such as its behavior under ordinal sums and the survival operation. We also study checkerboard copulas in the range of $\Psi$ and matrices associated to them.

Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13598v1 Announce Type: new Abstract: We analyze distributional drift in nonstationary weighted risk minimization by decomposing the excess risk into estimation, drift, and approximation components. The drift error is commonly bounded through discrepancy-type quantities that control changes of the risk over classes of predictors. We instead relate the drift error directly to the movement of the best predictor within the model class and analyze its behavior in parametrized regression models. Our analysis shows that discrepancy-type quantities can be overly conservative: unlike our oracle drift, they may scale at a larger order than the resulting excess-risk contribution and can respond to changes in the risk surface that do not affect the optimal predictor. For linear regression, we characterize this gap sharply and combine the resulting drift bounds with estimation guarantees. We further extend the analysis to nonparametric regression.

Estimating ratio of variance components in a balanced one-way random effect model

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13489v1 Announce Type: new Abstract: This paper considers the problem of estimating the ratio of variance components of a balanced one-way random effects model. Existing estimators of ratio of variance, such as the ANOVA and maximum likelihood estimators, can take negative values and are inadmissible under quadratic loss. We therefore study the problem under a general class of scale-invariant loss functions. We characterize the class of scale-equivariant estimators of ratio of variance and obtain the best equivariant estimator. We then derive a class of estimators that dominate the BEE and extend this class to obtain further improved estimators. We propose a smooth improved estimator of ratio of variance. For interval estimation of ratio of variance, we derive an asymptotic confidence interval, bootstrap confidence intervals, a generalized confidence interval and a highest posterior density credible interval. The performance of the proposed improved point estimators and confidence interval procedures is assessed through an extensive simulation study. Finally, we provide a real data analysis for implementation purposes.

Brown's loss function and estimation of the scale parameter and the entropy in scale mixture models with unknown location

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13460v1 Announce Type: new Abstract: This paper deals with the problems of decision theoretic estimation of the scale parameter, $\sigma$, and the entropy (Shannon or Renyi) in general scale mixture models with unknown location. Employing Kubokawa's approach, under convexity of the loss $L(t)$ either in $t$ or in $lnt$, improved estimators of $\sigma$ are derived. If $L(t)$ satisfies an additional condition, the problem reduces to estimating $\sigma$ in the degenerate (scale mixture) model. As the entropy is a linear translation of $ln\sigma$, its estimation under a loss $L_0(u)$ amounts to estimating $\sigma$ under $L(t)=L_0(lnt)$, with the quadratic loss $L_0(u)=u^2$ and Brown's loss $L(t)=(lnt)^2$ being a typical case. Thus, in the case that $L_0(u)$ is convex improved estimators of the entropy are directly obtained from respective estimators of $\sigma$. The results are applied to scale mixtures of normal and exponential distributions, including the multivariate $t$ and multivariate Lomax distributions.

Finite-Sample Bounds for Fr\'echet Means of Dependent Data in Metric Spaces with Curvature Bounded Above

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13362v1 Announce Type: new Abstract: We prove finite-sample risk bounds for empirical quadratic and power Fr\'echet means in geodesic metric spaces with curvature bounded above for observations with arbitrary joint law. We compare the sample with exchangeable copies in which one observation is redrawn independently of the original sample and the others move to preserve the joint law. These displacements control the error, with no entropy or dimension assumptions. For quadratic Fr\'echet means, this yields a general ``coupling bound'' in any separable complete $CAT(\kappa)$ space, where for $\kappa>0$ the observations must lie in a closed convex set of circumradius below $\pi/(2\sqrt{\kappa})$. This bound is exact on the real line for nonnegatively correlated Gaussian observations and for comonotone functions of a common factor. We apply it in two settings. Under local dependence, the resulting risk bound grows linearly with the average size of the dependency neighborhoods. Under transport sensitivity and for bounded metric variances, summable sensitivities of the conditional laws to a change in one observation preserve the parametric mean squared error rate, while nonsummable polynomial decay gives explicit slower rates. We verify transport sensitivity for stationary reversible Markov chains with Wasserstein-contractive kernels and for bi-Lipschitz images of Gaussian sequences. In the more challenging setting of heavy-tailed, dependent data with possibly infinite variance, we consider power Fr\'echet means of order $\alpha\in(1,2)$. Under nonpositive curvature, we bound their $L^\alpha$ risk assuming only finite $\alpha$-th moments.

On Eigenvector Statistics of Large-Dimensional Sample Covariance Matrices with Applications

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12928v1 Announce Type: new Abstract: We study the eigenvector-weighted spectral statistics \[ T_n(\varphi,g)=p^{-1}tr\{\varphi(\boldsymbol{S}_n)g(\boldsymbol{\Sigma})\} \] of large-dimensional sample covariance matrices $\boldsymbol{S}_n$ with population covariance $\boldsymbol{\Sigma}$. These statistics combine functions of sample eigenvalues with sample--population eigenvector overlaps and arise in statistical losses that depend on both. As the dimension and sample size grow proportionally, we establish a joint central limit theorem for $\{T_n(\varphi_a,g_a)\}_{a=1}^r$ with multiple analytic test functions and population weights, centered by finite-dimensional deterministic equivalents. A key intermediate step is a joint Gaussian process limit for the weighted resolvent traces \[ m_n^g(z)=p^{-1}tr\{(\boldsymbol{S}_n-z\boldsymbol{I}_p)^{-1}g(\boldsymbol{\Sigma})\}. \] The limiting means and cross-covariances are expressed in terms of the population spectral distribution. We apply these results in two settings: one concerns the variance component of minimum-norm prediction risk, and the other concerns the Frobenius loss of fixed rotationally invariant covariance estimators. For fixed affine shrinkage rules, the loss means, variances, and cross-covariances have explicit formulas in terms of population spectral moments.

When is Hotelling's $T^2$ asymptotically $F$-distributed?

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12903v1 Announce Type: new Abstract: For Gaussian observations, a deterministic multiple of Hotelling's $T^2$ statistic has an exact $F$ distribution. This paper investigates when this approximation remains valid for an independent and identically distributed (i.i.d.) data matrix $\mathbf{X}\in \mathbb{R}^{p\times n}$ with a fixed, possibly heavy-tailed entry law $\xi$. Under symmetry and $\limsup_{n\rightarrow \infty} p/n x)=0$ when $p/n\rightarrow \gamma\in (0,1)$, and obtain the $F$ approximation as a consequence. Centered standardized Pareto laws show that the exponent $5/2$ is sharp for this universal absolute-tail sufficient condition, although balanced-tail nonsymmetric laws can retain the approximation at the boundary, which reveals that the asymmetry of the tails matters for the $F$ approximation.

Detecting Random Geometric Graphs with General Kernel

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12765v1 Announce Type: new Abstract: We study testing a random geometric graph with a fixed kernel against an Erd\H{o}s-R\'enyi graph with the same edge density. Under the null hypothesis, the graph has $n$ vertices and independent edges with probability $p$. Under the alternative hypothesis, latent points $X_1,\ldots,X_n$ are independent and uniform on $\mathbb{S}^{d-1}$, and edges are conditionally independent with probabilities $K(\langle X_i,X_j\rangle)$, where $p=\mathbb{E}[K(\langle X_1,X_2\rangle)]$. The goal is to determine a critical dimension $d_\star = d_\star(n,K)$: the total variation distance between the two graph laws tends to one for $d\ll d_\star$ and to zero for $d\gg d_\star$. For dense graphs, [BDER16] established $d_\star\asymp n^3$ for hard threshold kernels, whereas [MWX26] proved $d_\star\asymp n^{3/4}$ for smooth kernels with $K'(0)\ne0$. We connect these results by characterizing the detection thresholds for kernels that need not be differentiable at zero. We also determine the thresholds for smooth kernels whose first nonzero derivative at zero has finite order greater than one. Throughout these classes, signed triangle or quadrilateral counts attain the optimal detection threshold. For certain nondifferentiable kernels, quadrilateral counts are optimal while triangle counts are suboptimal.

Minimax Rates for Estimating Powered Sliced Wasserstein Functionals

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12740v1 Announce Type: new Abstract: We study the two-sample estimation of the powered Sliced Wasserstein functional under projected $r$-th moment assumptions. Let $N=n\wedge m$, where $n$ and $m$ are two sample sizes. We establish the minimax rates in the noncritical regimes. When $p 2p$ it is of order $N^{-1/2}$. In both cases, the natural plug-in estimator is minimax rate-optimal. At the endpoint $r=p$, the minimax risk is bounded away from zero, so uniformly consistent estimation is impossible. At the critical order $r=2p$, we obtain the exact worst-case rate of the plug-in estimator and a lower bound for the minimax risk, leaving a logarithmic gap between the lower and upper bounds. The exact minimax rate in this critical case remains open.

Amortised Inference through One-Step Implicit Sampling

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12679v1 Announce Type: cross Abstract: Efficient sampling from Bayesian posterior distributions in high dimensions remains a hard problem, despite advances in theory and algorithms. Multiple steps are usually required to draw unbiased samples, for example, iterations of an MCMC algorithm or integration steps in a diffusion-based amortised sampler. However, scalable one-step amortised inference remains a challenging open problem. In this work, we build upon recent progress in data-driven generative modelling to offer a possible solution for one-step amortised sampling. Our one-step implicit sampler (OSIS) uses short-time MCMC dynamics to define a local target for the evolution of an implicitly modelled distribution. In the asymptotic limit, the modelled distribution is a fixed point of the MCMC kernel and thus samples from the target. We analyse the convergence properties of OSIS and show connections with other generative modelling and sampling algorithms. We study various design choices and show that OSIS performs well compared to multi-step amortised samplers and non-amortised MCMC baselines while being far more efficient at sampling time.

Faithfulness Without Anchors: A Position Paper on the Structural Misalignments of Explainable AI Faithfulness Metrics for Feature Importance

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12493v1 Announce Type: cross Abstract: Explainable Artificial Intelligence (XAI) tools have often been presented as methods to increase trust in machine learning models by making aspects of their algorithms more human-understandable. However, evidence accumulated over the last decade points to an overall failure of this objective, instead promoting overreliance on incorrect predictions, which can subsequently lead to algorithmic aversion. Rather, XAI appears to function primarily as a debugging tool, useful for obtaining anecdotal insights into, for example, features learned by the model. One of the main issues underlying this limitation is that XAI methods often oversimplify the inner workings of the model, resulting in misalignment between the explanation and the model itself - a behavior referred to as unfaithfulness or infidelity. Faithfulness can be interpreted as the degree of approximation between an explanation and the model. Computing faithfulness in a rigorous manner would thus make it possible to quantify one of the various elements of trustworthiness of an explanation. However, existing metrics present significant limitations, making this quantification either infeasible or computationally expensive. In this position paper, we outline five major shortcomings of current faithfulness metrics and propose four possible avenues for research to bolster their reliability.

On the estimation and validity of AI time horizons---a statistical look at the METR plot

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12466v1 Announce Type: cross Abstract: METR's 50\% time horizon measures the human completion time of software tasks that an AI solves with 50\% probability, allowing AI capabilities to be expressed in interpretable units. On 228 tasks and 26 AIs, we recompute the time horizons using splines and item-response theory to relax the assumption that the AI difficulty of a task depends linearly on the log of human time. Our fitted spline can be interpreted as a function that \emph{converts} human time to AI difficulty; it is nearly flat in a region from 2--30 min but close to linear elsewhere. Hence, a time-horizon jump from 3 min to 30 min is much easier than one from 30 min to 5 hours despite the same multiplier of $10 \times$. Overall, we contribute time-horizon point estimates that perform better under a cross-validated suite of proper scoring rules, as well as diagnostic plots for assessing time horizons' construct validity. We suggest that time horizons be interpreted together with the diagnostic plots, especially as new time-horizon-based benchmarks are proposed or existing ones grow to include longer tasks.

Hitting-Time Bounds for Asynchronous Q-Learning

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13901v1 Announce Type: new Abstract: We study the last iterate of standard asynchronous Q-learning from a single trajectory of a finite Markov decision process. The trajectory follows a fixed behavior policy whose state--action chain is irreducible and may be periodic. For discount factor $\gamma$, write $H=(1-\gamma)^{-1}$, and let $\mu_{\min}$ be the minimum stationary state--action probability and $\mathfrak h_\star$ the largest expected hitting time of the reverse state--action chain. We prove that zero-initialized Q-learning with a constant step size achieves sup-norm error at most $\varepsilon$ with high probability using $\widetilde{O}(H^4/(\mu_{\min}\varepsilon^2)+\mathfrak h_\star)$ transitions, for $0<\varepsilon\le1$. The statistical term retains the quartic effective-horizon dependence of standard Q-learning, while initialization cost is additive in $\mathfrak h_\star$. For aperiodic behavior chains, a comparison with mixing time yields a transient term $\widetilde{O}(t_{\mathrm{mix}}/\mu_{\min})$. An empirical state--action count rule selects a constant step size for a subsequent training run and attains the same rate without prior knowledge of model parameters, target accuracy, or confidence level. The output is the last training iterate, with both stages included in the sample count. The proof uses two deterministic Bellman envelopes to separate statistical error from fixed-policy initialization error and adapts reverse-time hitting-cost compensation from TD learning to state--action propagation. An exploration lower bound holds for arbitrary predictable step sizes. Together with the existing statistical lower bound and its extension to pilot-selected constant steps, it yields matching mean-square rates up to logarithmic factors on the stated large-sample parameter classes.

Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13851v1 Announce Type: new Abstract: We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps. Our approach aligns the score-training objective with the sampling grid, allowing statistical estimation and numerical discretization errors to be analyzed together. Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations. For every smoothness index $\beta>0$, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence $\widetilde O_p(n^{-2\beta/(d_x+d_y+2\beta)})$ relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error $\widetilde O_p(n^{-\beta/(d_x+d_y+2\beta)})$. Here $n$ is the sample size, $d_x,d_y$ are the data and conditioning dimensions, and errors are averaged over the conditioning variable. The total-variation bound matches the rate established in existing conditional distribution-estimation theory, up to logarithmic factors.

Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13804v1 Announce Type: new Abstract: Gaussian process solvers for linear partial differential equations (PDEs) return posteriors rather than point estimates, but they condition only on equality information: the PDE residual, boundary data, and measurements. Many solutions of interest also obey inequality constraints, including nonnegativity, monotonicity, and absence of arbitrage, which equality conditioning cannot enforce. We prove that conditioning a Gaussian process prior jointly on linear equality observations and a finite-dimensional inequality event is equivalent to conditioning sequentially in terms of Borel measures on the solution space. The physics-informed posterior is therefore a valid prior for the inequality update at virtual points. The combined law is non-Gaussian yet computable through truncated-Gaussian moments, and neither the PDE conditioning nor the inequality update requires modification. We evaluated the construction on a Poisson benchmark, option-price surfaces, and air-quality fields. Under incomplete boundary data, a monotonicity constraint lowered the error of a two-dimensional Poisson reconstruction by $63\%$. On a real S&P 500 option chain thinned to $20$ retained quotes, no-arbitrage constraints reduced held-out extrapolation error by $22\%$ and cut the calendar-arbitrage rate from $10\%$ to $1\%$. On four real air-quality snapshots, nonnegativity reduced a Gaussian moment-based sub-zero-tail proxy by $74\%$ at the sparsest monitor count. Changes in mean accuracy and constraint diagnostics differed across data regimes. The probability of the noisy virtual constraint event under the equality posterior measures agreement with the specified bounds before the update. The construction turns admissibility from a post-processing step into conditioning information for probabilistic PDE solvers.

From Pixels to Privacy-Sensitive Features: An Information-Theoretic Framework for Reconstruction Bounds

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13768v1 Announce Type: new Abstract: What can an adversary recover from a model trained with DP-SGD? Its $(\varepsilon,\delta)$ guarantee does not answer this question directly. We derive a distortion bound that can be computed before training and applies even to an adversary who observes the parameter trajectory during training, knows every other training record and the population distribution from which the training records are drawn. The analyst may choose the representation in which error is measured, allowing the bound to target the aspects of reconstruction that are privacy-sensitive in a given application. Our information-theoretic framework separates two contributions: the information about a record revealed by training, measured through conditional mutual information, and the uncertainty already present in the data distribution, measured through source entropy. Rate-distortion theory combines them into a lower bound on the expected error of every reconstruction attack. For DP-SGD, the leakage bound depends only on the sampling rates and noise multipliers, while the source entropy is lower-bounded from a sample with finite-sample confidence. An orthogonal block construction keeps the resulting bound informative for high-dimensional images. We instantiate the framework in pixel space and in LPIPS feature space, obtaining, to our knowledge, the first lower bound on reconstruction distortion measured directly by LPIPS. On a range of image datasets the bounds establish non-trivial unavoidable expected reconstruction error within heuristically recommended privacy-budget ranges and beyond. Experiments compare the bounds with strong reconstruction attacks and identify the principal sources of the remaining slack.

How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13764v1 Announce Type: new Abstract: Prior-data fitted networks (PFNs) are trained to approximate the Bayesian posterior predictive distribution (PPD) of a synthetic prior, yet results about the approximation quality are surprisingly thin. Taking an empirical risk minimization perspective, we decompose the deployment error of PFNs into prior, context, and amortization error, and measure the latter against a reference PPD under a realistic prior. Results show that PFNs generally recover the targeted PPD very well. Nevertheless, we find that parts of the residual amortization error persist, especially in \textit{rare} settings under the prior pretraining distribution, even when scaling the model size, which manifests in disagreement between independently pretrained PFNs and leaves uncertainty about the predictor at inference time. As a remedy, we study multiple types of Bayesian model averages and find that these can consistently reduce this uncertainty and improve predictions up to full-size TabICLv2 models.

Not All Dimensions Are Equal: Outlier-Aware Attention Linearization with Grouped Quadratic Kernels

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13674v1 Announce Type: new Abstract: Linearizing softmax attention offers a route to efficient Transformer inference, but preserving pretrained attention remains challenging. We identify an important source of approximation error overlooked by standard linearization methods: a small number of outlier dimensions contribute disproportionately to query-key dot products and account for a large fraction of the approximation error. Motivated by this heterogeneity, we propose Outlier-Aware Attention Linearization (OAL), a dimension-aware method for constructing quadratic attention approximations. Starting from a second-order Taylor approximation, we introduce a Hadamard-product formulation that makes individual query-key contributions explicit. This formulation relaxes globally shared coefficients to support dimension-specific linear terms and cross-dimensional quadratic interactions while preserving separable evaluation. To retain this flexibility with fewer parameters, OAL groups dimensions with similar contribution scales to share coefficients, while allowing distinct treatment of the few outliers. The resulting positive quadratic kernel is calibrated against pretrained attention outputs and admits linear-time evaluation with respect to sequence length for fixed head dimensions. On Qwen2.5-0.5B, OAL reduces frozen-attention output relative MSE by approximately 8.9% compared with DiJiang. Replacing middle-layer attention modules and jointly fine-tuning the kernel coefficients with LoRA further lowers WikiText-103 perplexity from 31.71 to 27.50 compared with a learned global quadratic, while improving accuracy on PIQA, HellaSwag, and ARC-E. These results demonstrate the value of outlier-aware dimension grouping for both attention approximation and pretrained-model conversion. The code is available at https://github.com/wuqianyue09/OAL

A Critical Look at Power Sampling when Test Time Sharpening LLMs

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13653v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards (RLVR) has substantially improved LLM reasoning, yet growing evidence suggests it mainly performs distribution sharpening: concentrating probability mass on reasoning paths the base model already produces. Recent work therefore seeks RLVR's gains without needing reward signals, by sampling from the power distribution $\pi_\alpha \propto \pi_{\text{base}}^\alpha$ via Markov chain Monte Carlo or sequential Monte Carlo. We show that these samplers fail to converge to $\pi_\alpha$ under realistic compute budgets, and that their gains are largely recreated via simple Best-of-$N$ with appropriate grading . This suggests they succeed by selecting high-probability sequences, not by approximating $\pi_\alpha$, raising a natural question: is the power distribution itself a worthwhile target? We test this hypothesis directly by fine-tuning the base model to match $\pi_\alpha$, sidestepping sampler convergence issues entirely. Despite approximating the target far more faithfully than existing samplers, this strategy yields gains that are noisy and specific to certain models and sampling tasks. Together, our results suggest that the value of power sampling lies not in faithfully targeting $\pi_\alpha$, but in the simpler goal of extracting sequences the base model already deems likely.

CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13606v1 Announce Type: new Abstract: Correlation matrices combine nonlinear positive-definiteness constraints with a simultaneous row-column permutation symmetry. Their generation therefore involves two distinct problems. First, every output must remain on the correlation elliptope, irrespective of how its variables are ordered. Second, the generator must learn the domain-specific distribution occupied by empirical data inside that valid space. Existing financial image generators mix these problems: they learn ordered matrix entries and repair invalid draws afterward. We introduce CorrFlow, which separates them. A generalized Fisher transform maps full-rank correlation matrices bijectively to unconstrained coordinates, guaranteeing valid outputs without projection. A graph flow-matching network learns the empirical distribution in those coordinates and is permutation equivariant: reordering the variables only reorders the output. We compare a conditional CorrGAN reimplementation, image diffusion, and CorrFlow on $80\times80$ Taiwan equity matrices using five seeds per neural method. CorrFlow produces 100% valid draws without repair and obtains feature sliced-Wasserstein distance $.712\pm.141$, versus $4.339\pm.252$ for CorrGAN and $4.610\pm.191$ for image diffusion after their invalid outputs are projected back to the correlation space. It also improves this distance over historical lookup, while lookup retains higher local coverage. These results support the combined construction under the evaluated training budget; they do not establish superiority over fully tuned image models or isolate the contribution of each component.

Defence against the dark arts of distillation: Unsupervised discovery of subliminal learning

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13536v1 Announce Type: new Abstract: When a language model is distilled from a teacher that shares its base parameters, the student can inherit behavioural traits of the teacher---including misalignment---even from data that is semantically unrelated to the trait (Cloud et al., 2026). All existing defences require knowing the trait. We remove this requirement and prove that a subliminally transferred trait can be recovered from the parameter updates alone, without supervision, by exploiting a single asymmetry: the trait is expressed consistently across diverse datasets generated by the teacher, whereas task-specific and shared capabilities vary. The resulting estimator returns a weight-space direction that can be amplified to discover and interpret the trait or projected out to suppress it. Applied to the subliminal-learning benchmarks of (Cloud et al., 2026), our method recovers the transmitted animal-preference traits without any trait labels and suppresses their expression with almost no impact to task performance.

Model-free Bayesian Clustering and Multimodal Posterior Summarisation

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13397v1 Announce Type: new Abstract: We develop a model-free, noise-aware Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive Bayesian perspective. This avoids explicit likelihood-prior model specification, expensive MCMC sampling, and mode-seeking variational approximations, while accommodating irregular cluster shapes and enabling parallel generation of posterior draws. To interpret the posterior over high-dimensional, noise-aware clusterings, we introduce a Wasserstein-type summarization method. Using a novel noise-aware loss, this approach compresses the large collection of posterior draws into a small set of weighted representatives, capturing distinct cluster structures and noise assignments. Further, we marginalise the uncertainty in the density level, avoiding reliance on a specific choice. We establish theoretical properties of the proposed loss and guarantees for the level-marginal posterior approximation. Results demonstrate the framework's effectiveness in capturing clustering and noise uncertainty.

Fast Gradient-Based Approximation of Continuous Dynamic Time Warping

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13129v1 Announce Type: new Abstract: Dynamic Time Warping (DTW) is a common choice for measuring the discrepancy between time series. It proceeds by finding an optimal warping between timestamps through dynamic programming, which can be slow and is not differentiable. Consequently, several variants have been proposed. Among them, Soft-DTW proposes a smooth formulation of DTW, amenable to gradient computation, while Continuous-DTW (CDTW) introduces a continuous formulation through parametrizable warping functions. Yet, computational costs remain high for both methods and impractical for large datasets in modern machine learning pipelines. This paper revisits CDTW in several ways. After establishing its differentiability under mild conditions, we introduce FastCDTW, which is an efficient approximate solver with two different computational strategies: an exact closed-form scheme for piecewise-linear warping functions, and an unbiased Monte Carlo estimator for smooth ones, such as implicit neural networks. Both strategies provide gradients with respect to the warping function and the input time series, and the resulting algorithm is GPU-friendly. We demonstrate its benefits through its integration into more complex learning problems, including time series averaging, classification and deep domain adaptation.

Why Heavy-Tailed Weight Spectra Predict Model Quality

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13123v1 Announce Type: new Abstract: A solid understanding of the predictive success of deep neural networks (DNNs) remains elusive. For example, while many data-dependent metrics exist that seek to predict model quality of DNNs, these metrics may be expensive to compute for large datasets and/or may be impossible to compute when training datasets are not released. A practical and effective predictor of model quality involves analyzing DNN weight matrices, as prior work has established that heavy-tailed spectral distributions in trained weight matrices can be strongly predictive of model quality. However, such metrics lack a rigorous statistical justification. In this work, we aim to understand why these metrics perform well, from a statistical perspective. To do so, we employ a probabilistic framework to derive the marginal likelihood for a DNN, evaluated using only the final layer weights. Across large-scale convolutional DNNs and LLMs, we find that this marginal likelihood predicts model quality. To understand the role heavy-tailed spectra play in predictive performance, we derive the limiting log-marginal likelihood for spectra that follow the (heavy-tailed) High-Temperature Marchenko-Pastur (HTMP) distribution. We show that this limiting quantity is convex in a heaviness parameter, and we derive an optimal heaviness that empirically predicts over-fitting for large-scale DNNs.

Scan-Parallel Variational Inference for event-driven Latent Jump Models

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12986v1 Announce Type: new Abstract: Continuous-time latent state-space models are widely used for irregularly observed time series, typically representing uncertainty through a random initial state followed by smooth ordinary differential equation (ODE) dynamics, or Brownian perturbations accumulated by a stochastic differential equation (SDE). While these constructions are natural for smooth or diffusive systems, they do not directly encode a finite set of unobserved shocks whose timing, magnitude, and effect on memory are themselves uncertain. We instead introduce latent jump models (LJMs): the latent state follows closed-form deterministic dynamics between Poisson-driven event times and undergoes a learned instantaneous jump at each event, with state-dependent intensity and mark distributions. This defines a time-homogeneous Markov process whose jumps are intrinsic state transitions rather than numerical integration steps. For training, we derive a tractable event-augmented path-space evidence lower bound (ELBO) and introduce Scan-Parallel Variational Inference (SPVI): an observation-conditioned variational posterior samples the complete latent event configuration before the state recurrence is evaluated using triangular affine scans. This enables fast and scalable training for LJMs in logarithmic temporal depth. Across synthetic stochastic systems and real irregular time series, LJMs remain competitive with continuous-time latent baselines in forecast accuracy, often with fewer latent updates than numerical solver evaluations, while training one to two orders of magnitude faster than the sequential baselines.

Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12924v1 Announce Type: new Abstract: We study dictionary learning for probability measure-valued data by embedding measures into Hilbert spaces using features derived from optimal transport geometry. We learn data-adapted dictionaries through sparse autoencoder parameterizations, producing fast, scalable representations of probability measures as sparse finite-dimensional codes. The resulting framework combines the rich, geometric structure of optimal transport with the interpretability and efficiency of sparse representation learning. We demonstrate its utility across diverse data modalities, including hyperspectral images, geometric point clouds, and document embeddings in large language model latent spaces. We also prove generalization bounds for sparse dictionary learning objectives on broad classes of $L^2$-valued measure embeddings, expressed in terms of the metric complexity of the atom class. For optimal transport and entropic transport map dictionaries, we derive new covering number bounds that yield explicit rates. Together, our computational and theoretical results support a new, scalable model for representation learning in the space of probability measures via embedding into Hilbert spaces.

Beyond Second-Order Information: Paid Logistic Regression with Noisy Features

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12919v1 Announce Type: new Abstract: We consider online binary prediction with paid stochastic features, where the learner can spend resources to obtain better observations of the underlying features. This setting is motivated by applications such as medical testing, where additional cost can provide more precise measurements of patient's features for predicting a binary outcome. At each round, a latent feature is drawn i.i.d., the response is generated through a logistic model, and the learner chooses how much to pay before observing a noisy version of the feature. The goal of learner is to jointly control prediction loss and acquisition cost. In contrast to the former result on the online linear regression with paid features, covariance information alone is no longer sufficient: two noise distributions with the same covariance may induce different optimal logistic losses, and lower variance can even lead to higher loss. Under a structural ordering in which larger payments yield better observations by removing independent noise, we obtain $\widetilde O(\sqrt{T})$ regret when the noise structure is known and $\widetilde O(T^{2/3})$ regret when it is unknown, with matching lower bounds up to logarithmic factors.

Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12894v1 Announce Type: new Abstract: Determinantal point processes (DPPs) model subset selection probability with repulsion, but many applications also exhibit attraction arising from pairwise relations or shared latent structures. Nonsymmetric DPPs (NDPPs) capture both effects, but their kernels are difficult to interpret and specify. We propose the determinant-ratio point process (DRPP), which models repulsion and attraction via a ratio of the determinants of two symmetric positive-definite kernels. This formulation preserves the feature-based interpretation of standard DPPs while allowing the two effects to be specified separately. Furthermore, we introduce an auxiliary-variable representation that enables efficient MCMC sampling and yields tractable expectation formulas for key statistics including the normalizing constant, which together facilitate maximum-likelihood learning. We theoretically characterize the interaction structures well suited to DRPPs: for clustered attraction with $C$ latent groups, DRPPs exactly realize the target pairwise interactions with an attraction rank $C$, whereas NDPPs can require a rank that grows with the number of items given the same repulsion component. Conversely, nontransitive pair-specific attraction may require compensation through the DRPP repulsion kernel. Experiments support these predictions, showing that DRPPs fit transitive attraction with substantially fewer parameters than NDPPs.

Universal Bounds for Self-Normalized Kullback-Leibler Estimation

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12851v1 Announce Type: new Abstract: This work studies an entropy-based estimator of Kullback-Leibler (KL) divergence constructed from normalized importance weights. We prove a universal finite-sample bound showing that its expectation can exceed the target-proposal KL divergence by at most $\log 2$ for any sample size. We then characterize the KL divergence between the distribution induced by importance-weighted resampling and the proposal, showing that it is upper bounded by both the expectation of the entropy-based estimator and the target-proposal KL divergence. Importantly, these bounds require neither bounded importance weights nor finite higher moments. We apply these results to test-time alignment of generative models via Soft Best-of-$N$ sampling, an importance-sampling-based scaling technique proposed by Verdun et al. (2025), and to relative entropy coding, obtaining finite-sample policy-divergence certificates and moment-free bounds on coding cost.

Typical Healthcare Pathways as a Basis for Admixture Modeling of Patient Trajectories

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2606.14587v2 Announce Type: replace Abstract: Background: Understanding whether patients follow similar or distinct patterns of care is important for characterizing clinical practice, identifying patient subgroups, and supporting quality improvement. However, routine healthcare trajectories are difficult to compare directly because patients may differ in their diagnostic workup, treatment sequencing, timing of clinical events, and documentation practices. Despite this variation, trajectories often contain recurring patterns at the cohort level. Methods: To address this challenge, we present a framework that explicitly separates cohort-level typical pathway identification from patient-level inference. At the cohort level, we derive an interpretable representation of care processes using a rule-based algorithm to identify typical healthcare pathways, resulting in a compact pathway graph. These pathways are then modeled as Markov chains and used as structured components in an admixture model, allowing each patient to be represented as a probabilistic mixture of typical pathways rather than being assigned to a single pathway component. The resulting admixture weights provide a compact representation of patient trajectories for subgroup characterization. We further assess the stability of the identified pathways and inferred admixture representations across multiple train-test splits. Results: Across train-test splits, the framework demonstrated consistent pathway structures and patient-level mixture patterns. Applied to routine care data from prostate cancer patients undergoing radical prostatectomy, the framework identified interpretable care patterns and supported the identification of patient subgroups with similar clinical event patterns. Conclusion: Overall, the proposed framework provides an interpretable and stable approach for summarizing treatment pathways and characterizing patient subgroups in real-world practice.

Active Sequential Signal Detection with Asynchronous Decisions

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2604.04755v2 Announce Type: replace Abstract: The problem of quickly detecting signals among multiple sequentially observed data streams, subject to constraints on the familywise false-alarm and missed-detection probabilities, is considered under an active sampling setup where only one stream can be sampled at each time instant. Under this setup, it is in general impossible to minimize, even asymptotically, the expected decision time simultaneously for every stream. We therefore consider minimizing the expected time until either the kth signal declaration or termination simultaneously for every k. We first establish non-asymptotic lower bounds for these criteria. For k > |B|, where B denotes the true subset of signals, we show that these lower bounds are attained asymptotically as the error levels vanish by any policy that stops sampling and makes a decision for each stream according to a local Sequential Probability Ratio Test. For 1 <= k <= |B|, however, the performance depends critically on the sampling rule, and we propose one with a simple exploration mechanism that prevents switching away from signals prematurely because of early unfavorable observations. We show that, under a mild relative-rate condition on the two error levels, the resulting policy attains all the lower bounds simultaneously. Numerical studies are presented to compare the proposed policy with an oracle policy and a follow-the-leader policy.

Coherent Information Deletion: Bayesian, Generalized Bayesian and Possibilistic Unlearning

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2602.09061v4 Announce Type: replace Abstract: Bayes' theorem admits an information processing interpretation due to Zellner (1988): under the Shannon information criterion, the posterior is the unique rule that processes prior and data information without information loss. We revisit these ideas from the perspective of information deletion. Given a posterior based on a complete dataset, what distribution should replace it when a subset of the data is removed? For ordinary Bayesian inference, we show that the corresponding information deletion objective is uniquely minimized by the leave-data-out posterior. We then extend the framework beyond likelihood-based inference from Bayes to the generalized Bayesian updating of Bissiri et al.(2016} based on loss functions. Requiring deletion to be coherent under sequential removal of loss contributions yields a deletion rule that exactly recovers the generalized posterior based only on the retained information. We further develop an axiomatic theory, beyond probabilistic inference, for possibilistic deletion and show that the same information-deletion perspective leads to a principled rule for exact possibilistic unlearning. Finally, restricting these exact deletion principles to tractable families leads naturally to variational Bayesian, generalized Bayesian, and maxitive possibilistic unlearning.

Reliability-Targeted Simulation of Item Response Data: Solving the Inverse Design Problem

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2512.16012v3 Announce Type: replace Abstract: Monte Carlo studies of item response theory (IRT) methods often leave the information level implicit in the choice of item parameters. Designs with the same sample size and test length can therefore represent quite different measurement conditions. We develop a calibration procedure that makes the information level an explicit design choice. The target is an information-based reliability index derived from population mean test information. Before generating responses, we solve for a common multiplier on item discriminations, keeping difficulties, test length and the reference population fixed. The R package IRTsimrel implements the procedure, allowing researchers to compare methods across chosen information levels or compare designs at a common target. In an item-level treatment-effect simulation, power increases across targets, while excess rejection from ignoring item-effect variation persists. These comparisons show how targeting helps distinguish findings that depend on the chosen information level from those that persist across the studied range.

SAT-sampling for statistical significance testing in sparse contingency tables

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2511.05709v2 Announce Type: replace Abstract: Exact conditional tests for contingency tables require sampling from fibers with fixed margins. Classical Markov basis MCMC is general but often impractical: computing full Markov bases that connect all fibers of a given constraint matrix can be infeasible and the resulting chains may converge slowly, especially in sparse settings or in presence of structural zeros. We introduce a SAT-based alternative that encodes fibers as Boolean circuits which allows modern SAT samplers to generate tables randomly. We analyze the sampling bias that SAT samplers may introduce, provide diagnostics, and propose practical mitigation. We propose hybrid MCMC schemes that combine SAT proposals with local moves to ensure correct stationary distributions which do not necessarily require connectivity via local moves which is particularly beneficial in presence of structural zeros. Across benchmarks, including small and involved tables with many structural zeros where pure Markov-basis methods underperform, our methods deliver reliable conditional p-values and often outperform samplers that rely on precomputed Markov bases.

A Moment-assisted Approach for Improving Subsampling-based MLE with Large-scale data

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2309.09872v5 Announce Type: replace Abstract: The maximum likelihood estimation is computationally demanding for large datasets, particularly when the likelihood function includes integrals. Subsampling can reduce the computational burden, but it often results in efficiency loss.This paper proposes a moment-assisted subsampling (MAS) method that can improve the estimation efficiency of existing subsampling-based maximum likelihood estimators.The motivation behind this approach stems from the fact that sample moments can be efficiently computed even if the sample size of the whole data set is huge.Through the generalized method of moments, the proposed method incorporates informative sample moments of the whole data. The MAS estimator can be computed rapidly and is asymptotically normal with a smaller asymptotic variance than the corresponding estimator without incorporating sample moments of the whole data. The asymptotic variance of the proposed estimator depends on the specific sample moments incorporated. We derive the optimal moment that minimizes the resulting asymptotic variance in terms of Loewner order. The proposed MAS estimator can achieve the same estimation efficiency as the whole data-based estimator when the optimal moment is incorporated. Numerical results demonstrate the promising performance of the proposed method in both estimation and computational efficiency compared with existing subsampling methods.

Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13656v1 Announce Type: cross Abstract: Latent field models are essential for spatial statistics, but the posterior distribution of the latent field, even with a Gaussian process (GP) prior, is analytically intractable whenever the likelihood is non-Gaussian. Existing approximations are either too slow or too restrictive for large non-Gaussian datasets. We present a scalable variational inference framework that mirrors the sparse nearest-neighbor autoregressive structure of the prior in the variational family, uses normalizing-flow conditionals for expressiveness, and amortizes all variational parameters via a single shared neural conditioner. Doubly stochastic optimization with reduced ancestor sets achieves polylogarithmic complexity per iteration.

From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12946v1 Announce Type: cross Abstract: Comparing distributions under severe sample imbalance requires effectively using abundant majority observations while retaining sensitivity to differences involving the smaller sample. This challenge is particularly relevant for complex, non-Euclidean data, such as graphs, whose structural characteristics call for flexible testing procedures. Classifier two-sample tests (C2STs) provide such flexibility, but existing procedures are primarily designed for balanced or comparably sized samples. In this paper, we study C2STs in a highly imbalanced regime, and show that severe sample imbalance may substantially degrade testing performance. Different from conventional imbalanced learning approaches that treat sample imbalance merely as a nuisance for classifier training, we turn it into a source of repeated testing evidence. Building on this insight, we propose an Enhanced Imbalance-Aware Deep Classifier Two-Sample Test (EIAD-C2ST), a classifier-agnostic framework designed for sample imbalance that accommodates diverse data modalities by tailoring classifiers to data structure. For computationally expensive deep classifiers, we further develop a scalable representation-amortized implementation strategy. Theoretically, we establish rigorous guarantees on asymptotic size and characterize conditions for power consistency, allowing the imbalance ratio to diverge. We demonstrate the empirical gains using simulations and an application to blockchain forensics. The results reveal that the majority-sample surplus, when properly leveraged, can be organized into useful statistical evidence, rather than an obstacle, for distributional comparisons with complex data.

Two-way Guidance: Simultaneous Learning of Summary Statistics for Generative Bayes

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12850v1 Announce Type: cross Abstract: Bayesian simulation-based inference (SBI) can struggle to recover increasingly concentrated posteriors as observation size grows. We consider learning sufficient summary statistics jointly with the posterior as a general principle for scalable inference in various SBI methods. A common measure taken in SBI is dimension reduction through predetermined summaries, which may partially discard posterior information. Our approach instead imposes structure on how the posterior learner depends on a learned summary (e.g., affinity), and learns the summary simultaneously with the posterior. We identify an important mechanism named two-way guidance: under a structural restriction on the summary, the posterior sufficiency of the learned summary simplifies posterior learning, whereas a suitable posterior objective guides the learned summary towards posterior sufficiency. This mechanism explains a counterintuitive finding that the structural restriction on the summary statistics improves posterior learning, rather than limit its performance. We establish theoretical guarantees on both posterior estimation error and the learned summary's departure from sufficiency, thus identifying conditions on the simulation budget for recovering increasingly concentrated posteriors as observation size grows.

SLICE: Sequential Likelihood-Free Inference via Conformal E-Values

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13855v1 Announce Type: new Abstract: Many scientific models can be simulated but have intractable likelihoods, making frequentist uncertainty quantification difficult. We construct exact anytime-valid confidence sequences for the parameters of such models. At each observation, fresh simulations from each candidate null conformalize a positive predictable score into a conditional e-value; their product is a test martingale, which we invert over the parameter. Validity holds for any such score, whatever its accuracy. We show that the oracle likelihood-ratio score maximizes expected log growth, which motivates approximating it with an amortized neural ratio estimator. On synthetic benchmarks, an audit of model routing in an LLM API, and microlensing data, the resulting confidence sequences stay valid under continuous monitoring, where fixed-sample methods do not, and neural scores remain competitive with exact likelihood ratios and application-specific scores.

Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13642v1 Announce Type: new Abstract: Circular data recorded over time, such as wind direction, are increasingly observed in intervals rather than as single point-valued observations, yet no existing framework accommodates data that are simultaneously circular, interval-valued, and temporally dependent. Time series models for point-valued circular data, including recently proposed score-driven approaches, assume that each observation is a single angle. This paper addresses this gap by proposing a dynamic conditional score framework for interval-valued circular time series. The lower and upper boundary sequences of the observed intervals are treated as circular time series governed by score-driven dynamics, which preserves the periodicity of the circular domain and the dependency of boundaries, in which the boundaries are coupled through a toroidal distribution and a jointly derived score. Maximum likelihood estimation is discussed, and their finite-sample performance is evaluated through simulation. An application to interval-valued wind direction data illustrates the practical value of retaining the interval structure within a fully rotationally invariant circular framework.

Kernel-based External Validity of Experimental Studies

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13625v1 Announce Type: new Abstract: The external validity of a study is the extent to which its findings generalize to unseen experimental conditions, such as datasets. We formalize the results of a study together with its research question, and define external validity as the probability that two independent and same-sized replications of the study produce results whose maximum mean discrepancy (MMD) is below a given tolerance. This approach, centered on the choice of a space of results and of an appropriate reproducing kernel for the MMD, is flexible enough to be deployed on multiple different types of results and research questions. Additionally, we establish an asymptotic power-law relation between the size of a study and the quantiles of the MMD, which we use to estimate the desired size of an externally valid study from a small-scale preliminary study. We deploy our framework to rankings with ties and discuss kernels suited to different research questions. Experiments on existing case studies and on a simulated newly designed study illustrate the applicability of the framework. We release our code as part of the genexpy Python module.

How Many Significant LISA?: A multiple testing correction

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13472v1 Announce Type: new Abstract: In spatial data analysis, global measures of spatial correlation provide useful insights into the general spatial patterns, but fail to capture local variations. Local Indicators of Spatial Association (LISA) address this limitation by identifying local clusters and spatial outliers, offering valuable applications in many fields of research such as public health, urban planning and environmental monitoring, to name only a few. However, the application of LISA tools in hypothesis testing is undermined by the presence of the multiple testing problem which dramatically increases the risk of committing Type I errors especially when dealing with very large datasets. Standard corrections procedure (like, e. g., Bonferroni and Benjamini-Hochberg procedures) fail to consider the spatial dependence among the various LISA tests and, furthermore, they are overly conservative. This paper proposes an adjustment that, by incorporating the notion of the "effective sample size", improves statistical inference balancing false discovery rate control and statistical power.

Arctan-skewing: a new skewing scheme on the hypertorus

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13310v1 Announce Type: new Abstract: In this paper we propose and study arctan-skewing, a general approach to skew any symmetric distribution on the unit hypertorus. Arctan-skewing retains the main advantages of the popular sine-skewing mechanism, but improves on it by overcoming its two major limitations. These are a condition on the skewness parameter and a singular Fisher Information matrix in the vicinity of symmetry when combined with well-known symmetric models from the literature such as the circular von Mises or bivariate Cosine models. Arctan-skewing thus represents a compelling alternative to model skewed data on the circle and torus, notably from the field of protein bioinformatics. After a thorough investigation of its stochastic properties, we present a maximum likelihood estimation procedure and devise optimal tests for symmetry against our new class of skewed alternatives. Finally we show that arctan-skewed models better fit protein data compared to their sine-skewed counterparts.

Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13290v1 Announce Type: new Abstract: Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinearly on multivariate state variables. Random Fourier features provide a flexible and computationally efficient approximation to the nonlinear boundary function. A two-stage procedure first estimates the induced regime classification using a smooth surrogate and then refits the structural parameters by hard-threshold OLS. We establish convergence of the first-stage regime classification and show that its estimation error is asymptotically negligible for the second-stage refit, yielding oracle equivalence. We further develop a dependent-multiplier bootstrap Sup-Wald test for detecting the existence of regime effects when the boundary is unidentified under the null, and establish its asymptotic validity. Simulations demonstrate accurate regime recovery, near-oracle performance of the proposed estimator, and satisfactory finite-sample behavior of the Sup-Wald test. An application to postwar U.S. unemployment data provides strong evidence of regime dependence, while the estimated nonlinear change plane identifies a distinct stress regime characterized by significant shifts in short-run unemployment dynamics.

Neural Estimation of Summary Statistics for Simulation-Based Inference with Non-Asymptotic Guarantees

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13031v1 Announce Type: new Abstract: Simulation-based inference (SBI) enables Bayesian inference when a simulator is available but the likelihood is intractable. Modern SBI methods train neural networks on simulated data to obtain an amortized approximation of the posterior, making inference for new observations fast. A central challenge in SBI is to extract informative, low-dimensional summary statistics; without them, performance can degrade rapidly as the observation dimension grows. We therefore highlight summary learning as a critical component of SBI and propose a general framework that jointly learns a neural-network-parameterized summary and an amortized posterior estimator. We further introduce a local refinement strategy that adapts the amortized estimator to a specific observation, thereby reducing the amortization gap. Both amortized training and local refinement accommodate implicit posterior estimators without tractable densities. On the theoretical side, we analyze the finite-sample behavior of the joint learning procedure through the lens of nonparametric conditional distribution estimation, and show on representative examples how low-dimensional summaries can mitigate the classical curse of dimensionality. Empirically, our results support this motivation and demonstrate favorable performance relative to existing methods.

Spatial Prediction with Guided Diffusion

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12967v1 Announce Type: new Abstract: Spatial prediction is a critically important task in data analyses that involve spatially or spatio-temporally-referenced data. It is commonly carried out using hierarchical models, which comprise a process model describing the latent process of interest, and a data model describing how the process is observed. The target quantity is the predictive distribution, which is the conditional distribution of the latent spatial process given the observed data. Unfortunately, the predictive distribution is rarely available in closed form and can be difficult to sample from. Here, we show how recent developments in guided diffusion modelling from machine learning can address a wide class of problems in spatial prediction when the likelihood function derived from the data model is known and differentiable, possibly after relaxation. To show the versatility of the approach, we apply it to both Gaussian and non-Gaussian process models and a variety of data models that describe direct partial observations, linear and areal aggregates, counts, right censoring, and area-exceedance functionals. Where possible, we validate the framework against exact and Markov-chain-Monte-Carlo (MCMC)-derived predictive distributions. We demonstrate our approach on several simulation studies and in a controlled experiment of methane-flux inversion over the UK and Ireland. We show that guided diffusion can sample from the correct predictive distribution in a variety of settings, that it can be applied to models where MCMC is intractable, and that it scales well with the dimensionality of the latent process.

Latent-Class Poisson-Lognormal Mixed Models for Clustering Multivariate Longitudinal Count Data

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12860v1 Announce Type: new Abstract: Multivariate longitudinal count data arise in biological studies, where responses may be over-dispersed, correlated within subjects and over time, measured at irregular times, and exhibit unobserved subgroup structure. Our goal was to develop a model that can accommodate over-dispersion, longitudinal dependence, cross-outcome dependence, covariate effects, irregular observation times, and covariate-dependent latent-class membership. We propose a latent-class Poisson-lognormal mixed model for clustering heterogeneous multivariate count trajectories. Estimation is performed using a variational EM algorithm designed for scalable inference. Simulation studies show accurate parameter estimation, strong latent-class recovery, and reliable selection of the number of classes, as compared to state-of-the-art approaches. We also applied the proposed approach to longitudinal neutrophil RNA-seq data from hospitalized COVID-19 patients as an illustration. The proposed framework provides a flexible approach for clustering complex longitudinal biological count data. Implementation code is available at https://github.com/PengqiLiu-Mc/latent-class-mpln-mixed-models.

Semiparametric Regression Based on Zero Altered Models

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12812v1 Announce Type: new Abstract: We develop a class of semiparametric zero-altered models (ZAMs) for count data, estimated through the generalized method of moments (GMM). The proposed framework extends the utility of ZAMs by allowing for both under- and over-dispersion while preserving support on the entire set of natural numbers. This offers an alternative to other models that can experience computational challenges (e.g. Conway-Maxwell-Poisson) or whose supports can be truncated as functions of the parameter space (e.g. generalized Poisson). By formulating estimation through moment restrictions rather than full likelihood specification, the GMM approach provides substantial robustness against model misspecification. In particular, inference based on likelihood methods for parametric generalized linear models (GLMs), such as those built on Poisson, negative binomial, or related count distributions, can become unreliable when the assumed distributional form is violated, often leading to biased estimates and invalid inference. In contrast, our methodology requires only the first two moments of the distribution, ensuring consistent estimation even when higher-order distributional features are misspecified. We establish the asymptotic properties of the estimators, including consistency and asymptotic normality, under general regularity conditions. The flexibility of the approach is illustrated through both simulated experiments and real-data case studies, demonstrating superior performance relative to popular parametric GLMs, particularly in settings characterized by distributional misspecification. To facilitate practical adoption, we provide accompanying R functions for easy implementation, enabling practitioners to apply the proposed methods in applied settings without requiring bespoke programming.

Product Monte Carlo: Expectation Under a Product of Densities

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12702v1 Announce Type: new Abstract: Aggregating independently computed sub-sample inferences is a well-known challenge in large-scale Bayesian computation, federated learning, and opinion pooling. The core problem is to approximate a distribution whose density is proportional to a product of individual densities. We propose Product Monte Carlo (PMC), an algorithm for computing arbitrary expectations under a product of densities using only Monte Carlo draws from individual densities. We turn the intractable product expectation into a regression problem by expressing it through a family of computable conditional expectations. Besides the point estimate, our fully Bayesian regression formulation provides coherent uncertainty quantification and principled diagnostics. We establish theoretical guarantees on consistency and characterize convergence rates for the PMC estimator. Across simulated and real-data experiments varying the number, dimensionality, and heterogeneity of the component distributions, PMC achieves higher estimation accuracy, better-calibrated uncertainty coverage, and improved scalability at a lower computational cost than existing methods. In addition, PMC requires no density evaluation, making it applicable to simulation-based inference, as we demonstrate in an application with protein images.

bayprior: Structured Bayesian Prior Elicitation, Conflict Diagnostics, and Regulatory Reporting

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2609.16410v2 Announce Type: replace-cross Abstract: Bayesian clinical trials require a well-specified prior distribution, and regulators increasingly expect that specification to be documented, diagnosed for prior-data conflict, and shown to be robust to reasonable alternatives, yet few R tools connect the full workflow of prior construction, validation, and regulatory justification into a single package. We introduce bayprior, an R package and Shiny application that implements structured expert elicitation via quantile matching, moment matching, and the SHELF roulette method across six distribution families; linear and logarithmic expert opinion pooling with Bhattacharyya agreement diagnostics; derivation of meta-analytic-predictive (MAP) priors from historical trial data via random-effects meta-analysis; prior-data conflict assessment using the Box p-value, S-value (surprisal) surprise index, information divergence, Bhattacharyya overlap, and multivariate Mahalanobis distance; hyperparameter sensitivity analysis with tornado and influence heatmap visualisations; and robust, sceptical, and power prior alternatives. A regulatory reporting module generates self-contained HTML, PDF, or Word documents addressing expectations in the FDA's 2026 draft Bayesian methods guidance and in EMA guidance on incorporating external and historical information. The package is demonstrated on a synthetic oncology Phase II trial. bayprior is available on CRAN and includes a fully modular Shiny application for interactive use.

Neural posterior inference with state-space models for calibrating ice sheet simulators

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2512.09561v2 Announce Type: replace Abstract: Ice sheet models are routinely used to quantify and project an ice sheet's contribution to sea level rise. In order for an ice sheet model to generate realistic projections, its parameters must first be calibrated using observational data; this is challenging due to the nonlinearity of the model equations, the high dimensionality of the underlying parameters, and limited data availability for validation. This study leverages the emerging field of neural posterior approximation for efficiently calibrating ice sheet model parameters and boundary conditions. We make use of a one-dimensional (flowline) Shallow-Shelf Approximation model in a state-space framework. A neural network is trained to infer the underlying parameters, namely the bedrock elevation and basal friction coefficient along the flowline, based on observations of ice velocity and ice surface elevation. Samples from the approximate posterior distribution of the parameters are then used within an ensemble Kalman filter to infer latent model states, namely the ice thickness along the flowline. We show through a simulation study that our approach yields more accurate estimates of the parameters and states than a state-augmented ensemble Kalman filter, which is the current state-of-the-art. We apply our approach to infer the bed elevation and basal friction along a flowline in Thwaites Glacier, Antarctica.

Thyroid Nodule Segmentation in Ultrasound Images with Conformal Uncertainty Estimation

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13604v1 Announce Type: cross Abstract: Thyroid nodules affect a large proportion of the general population. Although most are benign, a non-negligible fraction is malignant. Ultrasound imaging is the primary diagnostic modality, and accurate nodule segmentation is a prerequisite for CAD systems to classify malignancy and assess metastatic risk.\\ In this work, we propose a thyroid nodule segmentation framework that integrates a DeepLabV3+, channel-attention modules and post-hoc conformal prediction, providing both accurate mask and pixel-level uncertainty estimates. We address thyroid ultrasound nodule segmentation as the first stage of a pipeline that also includes malignancy classification and metastatic risk prediction. We adopt DeepLabV3+, whose Atrous Spatial Pyramid Pooling (ASPP) captures multi-scale context, with an EfficientNet-B5 backbone for its accuracy-efficiency trade-off. Additionally, we test three channel-attention modules: Squeeze-and-Excitation, CBAM and Grouped Channel Attention (GCA), paired with two loss formulations (Dice-BCE and Boundary).\\ Since binary masks do not indicate prediction confidence, we wrap the trained model with a split conformal prediction layer that produces pixel-level uncertainty maps with statistical coverage guarantees.\\ We evaluate all configurations on the TN3K public benchmark using a fixed split and directly compare them with state-of-the-art methods. The plain backbone already improves upon previously reported results, with CBAM + Dice-BCE emerging as the best overall configuration.

Design-based effect sizes and their synthesis in randomized multiple-baseline experiments

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13001v1 Announce Type: cross Abstract: Effect sizes for single-case experimental designs usually rely on models for the baseline trend and the serial dependence, which are challenging to check with few sessions. We develop design-based effect sizes for multiple-baseline experiments with a randomized intervention onset. We define case-level and pooled standardized effects with potential outcomes and propose weighted estimators that are unbiased or asymptotically unbiased without an outcome model. The usual difference between phase means is generally biased when the untreated outcome changes over sessions. For research synthesis, we provide variance estimators and asymptotic confidence intervals that require no model for serial dependence, and variance formulas for planning. Simulations and three randomized studies of reading and writing interventions illustrate the methods.

Sequential Conformal Calibration under Recursive Selection

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.12937v1 Announce Type: cross Abstract: Conformal prediction provides finite-sample, distribution-free coverage guarantees that can support decision-making in specific settings. In multistage problems, earlier decisions determine the populations relevant to later calibration. When later scores are refit using earlier calibration results, reusing those cases for ranking need not preserve exchangeability with a surviving test case. We study sequential conformal calibration with a fresh fold at each stage: conditional on earlier folds, the selected fold scores and the surviving test score are exchangeable. This yields finite-sample coverage guarantees for every prefix of the decision sequence. For atomless survivor score distributions, we derive a universal Binomial-thinned Beta chain for the realized coverage process. Its law depends only on fold sizes and target levels, even under predictable refitting, and yields exact coverage slack, abstention probabilities, and calibration-conditional guarantees. We further characterize the tradeoff between freshness and data reuse. For fixed scores, strict-survivor reuse is exactly valid. For adaptive scores refit using past calibration data, reusing survivors can incur worst-case rank loss, while blocked designs provide an intermediate option between full reuse and stagewise fresh folds. As a case study, we apply the framework to serial multi-echelon inventory problem and propose a sequential conditional-quantile formulation. Each stock level is learned as a context-dependent quantile of cumulative demand among scenarios satisfying earlier no-backlog constraints. We connect these targets to common-shift stationarity and derive decision-level implications for the resulting calibrated policies. In a three-echelon simulation, fresh-fold refitting achieves 81.98% final-prefix coverage against an 81.82% target while reducing mean cost by 5.5% relative to the Bonferroni baseline.

Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13588v1 Announce Type: new Abstract: Uncertainty quantification for electric vehicle (EV) charging demand is essential to turn the increasing pressure of EV adoption on power systems into a source of flexibility. We study a large-scale dataset of public charging stations in Scotland, where demand exhibits a hierarchical structure, organized across multiple aggregation levels, from individual charging points to regional and national scales. The charging infrastructure is continuously evolving, with new stations deployed and existing ones occasionally removed, which calls for forecasting and uncertainty quantification methods tailored to this evolving structure. To address these challenges, we combine hierarchical forecasting with recent advances in conformal prediction with missing data. The conformal procedures considered produce valid prediction intervals at every node of the hierarchy and the algorithm CP-MNR-Nested successfully accounts for the time-varying hierarchical structure of the data.

Warning of infrastructure deformation anomaly through probabilistic analysis of InSAR observations

Mon, 12 Oct 2026 00:00:00 -0400

arXiv:2610.13552v1 Announce Type: new Abstract: Interferometric Synthetic Aperture Radar (InSAR) offers a low-cost, wide-area solution for near continuous infrastructure monitoring. However, translating InSAR observations into automated anomaly warnings remains challenging because displacements are relative, affected by uncertainty, and acquired along line of sight (LOS). We introduced a probabilistic warning framework that accounts for these factors. LOS displacements were modelled through a Gaussian distribution. A limit state function was defined to describe the displacement exceedance, and the time-dependent probability of exceedance was evaluated. Instead of a fixed threshold, warnings were identified through abrupt increases in exceedance probability. The framework was validated using three case studies of quay walls in Amsterdam, providing timely anomaly warnings and issued no warnings for the non-collapse case. Results demonstrate the potential of a probabilistic interpretation of InSAR time series for deformation anomaly warning.

A Theory of the Mechanics of Information: Generalization Through Measurement of Uncertainty (Learning is Measuring)

Mon, 12 Oct 2026 00:00:00 -0400

Minimax Rates for Learning Smooth Populations of Parameters

Mon, 12 Oct 2026 00:00:00 -0400

Posterior Consistency for Recovering Initial States in Nonlinear Subdiffusion Equations

Mon, 12 Oct 2026 00:00:00 -0400

How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?

Mon, 12 Oct 2026 00:00:00 -0400

Dense alternating sign matrices and imprecise copulas

Mon, 12 Oct 2026 00:00:00 -0400

The Harmonic Entropy Estimator: Minimax Optimality and Semiparametric Efficiency for Infinite Alphabets

Mon, 12 Oct 2026 00:00:00 -0400

Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate

Mon, 12 Oct 2026 00:00:00 -0400

The Order Mass Identity of Rooted Forests, with a Direct Proof of the Extended Aldous--Broder Theorem

Mon, 12 Oct 2026 00:00:00 -0400

An efficient stochastic generalized method of moments estimator for nonlinear moment models

Mon, 12 Oct 2026 00:00:00 -0400

Effective-dimension bounds in the central limit theorem for centered Euclidean balls

Mon, 12 Oct 2026 00:00:00 -0400

Transformer-Based Masked Diffusion Models Provably Learn Distributions with Latent Structure

Mon, 12 Oct 2026 00:00:00 -0400

On diagonal sections of Markov products of copulas

Mon, 12 Oct 2026 00:00:00 -0400

Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization

Mon, 12 Oct 2026 00:00:00 -0400

Estimating ratio of variance components in a balanced one-way random effect model

Mon, 12 Oct 2026 00:00:00 -0400

Brown's loss function and estimation of the scale parameter and the entropy in scale mixture models with unknown location

Mon, 12 Oct 2026 00:00:00 -0400

Finite-Sample Bounds for Fr\'echet Means of Dependent Data in Metric Spaces with Curvature Bounded Above

Mon, 12 Oct 2026 00:00:00 -0400

On Eigenvector Statistics of Large-Dimensional Sample Covariance Matrices with Applications

Mon, 12 Oct 2026 00:00:00 -0400

When is Hotelling's $T^2$ asymptotically $F$-distributed?

Mon, 12 Oct 2026 00:00:00 -0400

Detecting Random Geometric Graphs with General Kernel

Mon, 12 Oct 2026 00:00:00 -0400

Minimax Rates for Estimating Powered Sliced Wasserstein Functionals

Mon, 12 Oct 2026 00:00:00 -0400

Amortised Inference through One-Step Implicit Sampling

Mon, 12 Oct 2026 00:00:00 -0400

Faithfulness Without Anchors: A Position Paper on the Structural Misalignments of Explainable AI Faithfulness Metrics for Feature Importance

Mon, 12 Oct 2026 00:00:00 -0400

On the estimation and validity of AI time horizons---a statistical look at the METR plot

Mon, 12 Oct 2026 00:00:00 -0400

Hitting-Time Bounds for Asynchronous Q-Learning

Mon, 12 Oct 2026 00:00:00 -0400

Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models

Mon, 12 Oct 2026 00:00:00 -0400

Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints

Mon, 12 Oct 2026 00:00:00 -0400

From Pixels to Privacy-Sensitive Features: An Information-Theoretic Framework for Reconstruction Bounds

Mon, 12 Oct 2026 00:00:00 -0400

How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?

Mon, 12 Oct 2026 00:00:00 -0400

Not All Dimensions Are Equal: Outlier-Aware Attention Linearization with Grouped Quadratic Kernels

Mon, 12 Oct 2026 00:00:00 -0400

A Critical Look at Power Sampling when Test Time Sharpening LLMs

Mon, 12 Oct 2026 00:00:00 -0400

CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope

Mon, 12 Oct 2026 00:00:00 -0400

Defence against the dark arts of distillation: Unsupervised discovery of subliminal learning

Mon, 12 Oct 2026 00:00:00 -0400

Model-free Bayesian Clustering and Multimodal Posterior Summarisation

Mon, 12 Oct 2026 00:00:00 -0400

Fast Gradient-Based Approximation of Continuous Dynamic Time Warping

Mon, 12 Oct 2026 00:00:00 -0400

Why Heavy-Tailed Weight Spectra Predict Model Quality

Mon, 12 Oct 2026 00:00:00 -0400

Scan-Parallel Variational Inference for event-driven Latent Jump Models

Mon, 12 Oct 2026 00:00:00 -0400

Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity

Mon, 12 Oct 2026 00:00:00 -0400

Beyond Second-Order Information: Paid Logistic Regression with Noisy Features

Mon, 12 Oct 2026 00:00:00 -0400

Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels

Mon, 12 Oct 2026 00:00:00 -0400

Universal Bounds for Self-Normalized Kullback-Leibler Estimation

Mon, 12 Oct 2026 00:00:00 -0400

Typical Healthcare Pathways as a Basis for Admixture Modeling of Patient Trajectories

Mon, 12 Oct 2026 00:00:00 -0400

Active Sequential Signal Detection with Asynchronous Decisions

Mon, 12 Oct 2026 00:00:00 -0400

Coherent Information Deletion: Bayesian, Generalized Bayesian and Possibilistic Unlearning

Mon, 12 Oct 2026 00:00:00 -0400

Reliability-Targeted Simulation of Item Response Data: Solving the Inverse Design Problem

Mon, 12 Oct 2026 00:00:00 -0400

SAT-sampling for statistical significance testing in sparse contingency tables

Mon, 12 Oct 2026 00:00:00 -0400

A Moment-assisted Approach for Improving Subsampling-based MLE with Large-scale data

Mon, 12 Oct 2026 00:00:00 -0400

Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

Mon, 12 Oct 2026 00:00:00 -0400

From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance

Mon, 12 Oct 2026 00:00:00 -0400

Two-way Guidance: Simultaneous Learning of Summary Statistics for Generative Bayes

Mon, 12 Oct 2026 00:00:00 -0400

SLICE: Sequential Likelihood-Free Inference via Conformal E-Values

Mon, 12 Oct 2026 00:00:00 -0400

Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction

Mon, 12 Oct 2026 00:00:00 -0400

Kernel-based External Validity of Experimental Studies

Mon, 12 Oct 2026 00:00:00 -0400

How Many Significant LISA?: A multiple testing correction

Mon, 12 Oct 2026 00:00:00 -0400

Arctan-skewing: a new skewing scheme on the hypertorus

Mon, 12 Oct 2026 00:00:00 -0400

Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference

Mon, 12 Oct 2026 00:00:00 -0400

Neural Estimation of Summary Statistics for Simulation-Based Inference with Non-Asymptotic Guarantees

Mon, 12 Oct 2026 00:00:00 -0400

Spatial Prediction with Guided Diffusion

Mon, 12 Oct 2026 00:00:00 -0400

Latent-Class Poisson-Lognormal Mixed Models for Clustering Multivariate Longitudinal Count Data

Mon, 12 Oct 2026 00:00:00 -0400

Semiparametric Regression Based on Zero Altered Models

Mon, 12 Oct 2026 00:00:00 -0400

Product Monte Carlo: Expectation Under a Product of Densities

Mon, 12 Oct 2026 00:00:00 -0400

bayprior: Structured Bayesian Prior Elicitation, Conflict Diagnostics, and Regulatory Reporting

Mon, 12 Oct 2026 00:00:00 -0400

Neural posterior inference with state-space models for calibrating ice sheet simulators

Mon, 12 Oct 2026 00:00:00 -0400

Thyroid Nodule Segmentation in Ultrasound Images with Conformal Uncertainty Estimation

Mon, 12 Oct 2026 00:00:00 -0400

Design-based effect sizes and their synthesis in randomized multiple-baseline experiments

Mon, 12 Oct 2026 00:00:00 -0400

Sequential Conformal Calibration under Recursive Selection

Mon, 12 Oct 2026 00:00:00 -0400

Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure

Mon, 12 Oct 2026 00:00:00 -0400

Warning of infrastructure deformation anomaly through probabilistic analysis of InSAR observations

Mon, 12 Oct 2026 00:00:00 -0400

Tree statistics improve neural simulation-based inference of epidemiological parameters over case counts alone

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10895v1 Announce Type: new Abstract: During an infectious disease outbreak, accurate estimates of epidemiological parameters such as the reproduction number and infection duration can inform the public health response. Recently, neural simulation-based inference (NSBI) methods have become popular for estimating these parameters due to lower computational costs and more input data flexibility than traditional methods. Input data modalities that have been evaluated independently in an NSBI framework include case counts and transmission trees. Here, we evaluate whether combining information from these two data types outperforms using information from each individually with NSBI. To do so, we simulated stochastic susceptible-infectious-recovered (SIR) outbreaks across a range of basic reproduction numbers (R0) and average infection durations (D) to generate training, validation, and testing datasets. We then calculated, for each simulated outbreak, summary statistics from case count trajectories and from transmission trees. Using these features, individually and in combination, we performed a type of NSBI called neural ratio estimation (NRE) to estimate R0 and D. We also calculated maximum likelihood estimates of the parameters by fitting a deterministic SIR model using the case count trajectory. All three NRE models outperformed the baseline method. Furthermore, incorporating tree summary statistics improved the estimation of both R0 and D over case count summaries alone. This suggests that trees provide valuable additional information for estimating epidemiological parameters above and beyond case counts alone.

BayesJudge: Uncertainty-Aware Bayesian Meta-Evaluation of Human and LLM Judgments

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11116v1 Announce Type: new Abstract: AI evaluation pipelines often produce conflicting judgments rather than clean labels. In pairwise LLM evaluation, this conflict is especially visible: disagreement can arise from ambiguous items, underspecified rubrics, heterogeneous or unstable human raters, or an LLM judge whose verdict changes when the response order is swapped. We propose BayesJudge, an online Bayesian meta-evaluation layer for conflicting human-LLM judgment streams. For each comparison, BayesJudge estimates a panel-relative posterior verdict distribution over the two responses, with a tie or ambiguity state when such labels are available. At the same time, it estimates rater-specific human confusion matrices and LLM presentation-order bias. The method uses tie-open labels to keep ambiguity observable and paired order-swapped judge calls to separate response quality from presentation effects. We formulate the exact online posterior recursion and use a scalable Rao-Blackwellized assumed-density SMC approximation for streaming inference. Controlled synthetic experiments demonstrate recovery of prespecified evaluator parameters and illustrate two protocol-level identifiability mechanisms: tie-open labels expose ambiguity mass, and order-swapped paired judgments separate item preference from position bias. On a real-world SummEval dataset, BayesJudge successfully detects systematic presentation-order effects in LLM judge outputs, infers distinct expert and crowdworker behavior signatures without rater metadata, and produces posterior uncertainty estimates that correlate with human disagreement. Our code is available at https://anonymous.4open.science/r/BayesJudge-0879.

Event-Aware Spatiotemporal Precipitation Forecasting with Geographic Context and Physics-Guided Regularization

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11211v1 Announce Type: new Abstract: Hourly precipitation forecasting involves several distinct statistical challenges, including spatially varying predictor-precipitation relationships, a strongly imbalanced precipitation distribution, and progressive degradation of precipitation event skill with increasing lead time. We develop a spatiotemporal forecasting framework that addresses these challenges through three complementary components: explicit geographic representation, event-aware learning for imbalanced precipitation, and weak asymmetric regularization derived from the atmospheric water budget. The physical information is treated as an asymmetric constraint rather than as an additional prediction target, designed to discourage physically unsupported precipitation attenuation without replacing the data-driven forecast. Experiments using ERA5 data across regional, enlarged domain, and spatial subset settings show that explicit geographic information improves spatial field prediction, while event-aware learning provides the most consistent gains in detecting moderate and heavy precipitation events. Physical regularization has a more selective effect, mainly reducing systematic underprediction over the enlarged domain while improving longer lead precipitation event prediction in the spatial subset experiment. These results indicate that the benefit of physical guidance depends on the available data regime and becomes most apparent when data-driven precipitation information deteriorates with increasing lead time.

How Much Does Submitting a Burst of Jobs Impact Waiting Time? An Analysis of the Jean Zay Workload Trace

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11703v1 Announce Type: new Abstract: This paper examines job waiting times on the Jean Zay supercomputer at IDRIS (Institut du D{\'e}veloppement et des Ressources en Informatique Scientifique http://www.idris.fr/), driven by the need to improve scheduling strategies for crossfacility scientific workflows. Drawing on large workload traces, we show that job waiting times are not independent of one another but are instead correlated through job bursts-batches of identical jobs submitted together, also called ``flurries''. We introduce a method for quantifying the effect of these bursts on waiting times, and find a strong Pearson correlation between waiting time and a job's rank within its burst. This correlation is above 0.8 for more than 40% of the jobs. We further derive an exact formula for the Slurm fairshare factor based on a convolution product, showing that the burst penalty operates on a much shorter timescale than fairshare itself-pointing to a distinct throttling mechanism specifically targeting bulk submissions. Once burst effects are accounted for, we use Welch's t-test to find that partition occupancy and number of requested cores have a significant effect on waiting time, though the effect is not significant for all partitions.

Regime-Aware Estimation of Large Equity Correlation Matrices: Tail-Pairwise Dependence and Dynamic Conditional Correlation Decomposition for Water and Energy Sectors

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12166v1 Announce Type: new Abstract: Equity correlation matrices are foundational to quantitative risk, yet the operational default of a single Gaussian-copula structure fit to the full sample has a structural defect: it forces asymptotic tail-independence and so cannot represent the joint moves that drive risk in stress episodes. We argue that the dependence of equity returns is not one object but three distinct under lower-tail, central, and upper-tail conditions, and that any estimator aimed at tail-sensitive applications should be regime-aware. We develop a decomposition that fits a dedicated dependence matrix to each regime, using a tail-dependence estimator grounded in multivariate regular variation in the two tails and a time-varying conditional-correlation model in the central regime, and recombines the three at the unconditional regime probabilities to form a steady-state matrix. The construction identifies tail-regime dependence that the Gaussian-copula benchmark structurally suppresses. Demonstrated on water- and energy-sector Exchange Traded Funds (ETF) constituents, the tail regimes reorganize the commodity partition produced by the central regime, identifying the pairs where the Gaussian-copula default systematically fails to identify joint extreme co-movement.

Mixup Barcodes for Topology-Aware Financial Decision Making

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12396v1 Announce Type: new Abstract: We present a topology-aware system based on mixup barcodes and persistent homology for financial decision making. The suggested approach uses topological summaries obtained from Takens delay embeddings of a univariate price series to quantify structural changes between reference and current market regimes. The 1-Wasserstein distance between persistence diagrams, a mixup barcode disruption index, and persistence entropy divergence are combined to provide a novel stress score. A Golden Cross trading method is dynamically modulated by this score, which transforms a binary buy/sell signal into a continuous position-sizing process. At embedding settings chosen by maximizing in-sample Sharpe over a 72-point grid, in-sample assessment on the S&P 500 and Bitcoin yields Sharpe ratios of 1.116 and 1.238, respectively, with much lower maximum drawdown compared with both Buy-and-Hold and the standard Golden Cross baseline. Our findings imply that topological summaries of market geometry include useful information that goes beyond traditional trend markers.

TypedBench: A Benchmark for Calibration, Framing Sensitivity, and Cost in System One Decision Models

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11392v1 Announce Type: cross Abstract: System One models output calibrated probabilities over typed answers such as categorical choices, ordinal levels, or binary outcomes, via a non-generative interface. Software can act on these probabilities through thresholds, cost-weighted choices, and escalation rules. Consequently, if these probabilities are miscalibrated or wording-sensitive, the software ma take unintended actions leaving human operators with no textual rationale to inspect. Current evaluations largely report accuracy and calibration on public classification datasets without a clear reference. We present TypedBench, a benchmark for typed decision models like Jev built from seven policy-labelled generators and nine evaluation suites. We report accuracy as median and range across paraphrases, and calibration error relative to the finite-sample noise floor of a matched, perfectly calibrated predictor. We assess probability quality through selective prediction, ordinal proper scoring rules, and realised cost under asymmetric cost matrices. We evaluate a hosted model, an open encoder, and a family of open decoders spanning 0.8B-9B parameters on identical items. The hosted model follows the stated policy but is wording-sensitive and systematically underconfident; under asymmetric costs, using its probabilities can be worse than taking its top answer. Decoders route exactly and are slow as options or questions are added. The decoder is least accurate on policy questions and degrades with more options. Overall, typed decision models must be evaluated jointly on policy adherence, wording robustness, probability quality, and induced decision outcomes.

Design-Based Validation Method of EHR Algorithms to Address Partial Verification Bias

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12059v1 Announce Type: cross Abstract: Electronic health record (EHR) phenotyping algorithms support clinical prediction, observational research, and quality improvement, but manual chart review for gold-standard validation is costly. For algorithms targeting rare outcomes, algorithm-negative patients often greatly outnumber algorithm-positive patients. We propose a design-based validation framework that fully verifies algorithm-positive patients and reviews a simple random sample (SRS) of algorithm-negative patients. Horvitz-Thompson estimators of false-negative (FN) and true-negative totals yield estimates of sensitivity, specificity, negative predictive value, positive predictive value, and accuracy. We derive finite-population-corrected variance estimators and confidence intervals (CIs), with sample-size planning for a prespecified CI half-width. An optional Phase 2 extension uses pilot data to assess whether risk-guided Neyman allocation may improve precision. In simulations, the design-based approach substantially reduced bias relative to naive verified-sample analyses and achieved near-nominal CI coverage. Adaptive allocation reduced root mean squared error and CI width when FNs were concentrated across risk strata, but offered little benefit when the risk signal was weak. We illustrate the framework using a breast cancer recurrence algorithm in 3,336 patients, with endpoint-specific algorithm-negative review budgets of 125, 150, and 175 charts. The framework combines SRS-based validation and precision planning with optional pilot-guided adaptive allocation.

Formalization and consistency of clone-censor-weight

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12377v1 Announce Type: cross Abstract: Target trial emulation has become a standard framework for causal inference from observational data. Within this paradigm, the clone-censor-weight (CCW) methodology provides a practical way to deal with complex treatment and adherence definitions when treatment regimes are not distinguishable at baseline. Despite its increasing use, the statistical interpretation of CCW remains limited. In this work, we formalize the CCW methodology from a statistical viewpoint based on admissible sets and stochastic interventions. We characterize the causal estimands targeted by CCW, establish consistency of CCW estimators under standard identification assumptions, and provide theoretical guarantees for bootstrap-based inference methods.

Spatial Dependencies in Item Response Theory: Gaussian Process Priors for Ecological and Cognitive Measurement

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2507.09824v4 Announce Type: replace Abstract: Measurement validity in Item Response Theory depends on appropriately modeling dependencies between items when these reflect meaningful theoretical structures rather than random measurement error. In ecological assessment, citizen scientists identifying species across geographic regions exhibit systematic spatial patterns in task difficulty due to environmental factors. Similarly, in Author Recognition Tests, literary knowledge organizes by genre, where familiarity with science fiction authors systematically predicts recognition of other science fiction authors. Current spatial Item Response Theory methods, represented by the 1PLUS, 2PLUS, and 3PLUS model family, address these dependencies but remain limited by (1) binary response restrictions, and (2) conditional autoregressive priors that impose rigid local correlation assumptions, preventing effective modeling of complex spatial relationships. Our proposed method, Spatial Gaussian Process Item Response Theory (SGP-IRT), addresses these limitations by replacing conditional autoregressive priors with flexible Gaussian process priors that adapt to complex dependency structures while maintaining principled uncertainty quantification. SGP-IRT accommodates polytomous responses and models spatial dependencies in both geographic and abstract cognitive spaces, where items cluster by theoretical constructs rather than physical proximity. Simulation studies demonstrate improved parameter recovery, particularly for item difficulty estimation. Empirical applications show enhanced recovery of meaningful difficulty surfaces and improved measurement precision across psychological, educational, and ecological research applications.

Opponent-Adjusted Evaluation of NFL Pass Protection and Pass Rush

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2604.01491v2 Announce Type: replace Abstract: Evaluating NFL pass protectors and rushers is difficult because observed win rates reflect both player performance and the difficulty of the blocking assignments each player faces. Using Hudl player coordinates and blocking annotations from the 2021 NFL regular season, we estimate blocker and rusher strength jointly from initial blocking matchups. A ridge-regularized Bradley--Terry model uses early pass rush wins and losses within 2.5 seconds of the snap, while a multinomial extension models full-play losses, wins, pressures, and sacks. To summarize full-play performance, we use the outcomes' conditional associations with offensive expected points added (EPA) to weight predicted probabilities, giving ratings of expected disruption produced by rushers or allowed by blockers. In held-out Weeks 16--18, the early and final models reduce log loss by 4.5% and 3.6%, respectively, relative to historical matchup baselines whose smoothing strengths are selected by cross-validation; 95% game-bootstrap intervals for both reductions are above zero. The resulting ratings place observed success in the context of opponents and protection help, with game-bootstrap intervals quantifying sampling uncertainty in early strength and full-play disruption.

Day-Ahead Electricity Price Forecasting Using a Multivariate Group Lasso Method

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2605.27781v3 Announce Type: replace Abstract: Electricity price signals in modern power systems exhibit complex dependence structures that render forecasting inherently challenging. Our analysis of real-world electricity pricing signals reveals complex temporal group effects, whereby the influence of explanatory variables on electricity prices persists across consecutive blocks of time due to underlying economic, system, and operational drivers. In response, we propose a multivariate statistical method based on a Group Lasso formulation to jointly forecast the vector of day-ahead electricity prices (h = 1, ..., 24), by leveraging multi-feature temporal group effects. Our approach is evaluated on two full years of electricity prices from the California Independent System Operator (CAISO), demonstrating considerable improvements in point and probabilistic forecast metrics compared to a wide array of statistical and deep learning methods. Empirical analyses confirm the effectiveness of the proposed approach in modeling realistic group effects, maintaining both interpretability and low computational complexity. When retrospectively evaluated on test data from a recent international electricity price forecasting challenge, the proposed method ranked in second place, despite having access to significantly less information than competing approaches. Finally, the proposed method is independently validated against two operational electricity price forecasting systems in CAISO, demonstrating competitive predictive performance and practical relevance.

Testing Additivity of Lead and Benzo[a]pyrene-induced Neurotoxicity in Caenorhabditis elegans Assays

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2608.20496v2 Announce Type: replace Abstract: Exposure to environmental contaminants is a recognized cause of neurotoxicity, contributing to the onset of a broad range of neurological conditions. In realistic settings, such exposure involves com- plex mixtures, and the combined effect of their components may differ from what their individual effects would predict. Characterizing such interactions and testing them against a principled notion of additivity is central to assessing the neurotoxicological risk. We take up these questions for two widespread and independently neurotoxic pollutants, lead (Pb) and benzo[a]pyrene (BaP), through a novel C. elegans assay in which nematodes were subjected to single and joint exposures across a range of doses. Morphological damage is quantified on an ordinal scale at the level of individual dopaminergic neurons. To analyze these data, we model the full distribution of the ordinal response as a convex mixture between an unexposed and a maximally affected profile. The weight of this mixture varies with chemical doses, modeled flexibly via monotone splines and, for the joint effect, in a radial coordinate system. Additivity is assessed via a likelihood ratio test against established null models, and is calibrated via parametric bootstrap. Applied to the C. elegans assay, our analysis reveals a localized, asymmetric synergy between Pb and BaP, concentrated where moderate BaP meets high Pb exposure.

LLM Benchmarking via Representation Multi-task Learning

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.05613v2 Announce Type: replace Abstract: Quantifying and evaluating the capabilities of Large Language Models (LLMs) remains a fundamental challenge in modern data science and artificial intelligence. In this paper, we consider LLM evaluation based on their performance across items in multiple benchmark domains (e.g., mathematical reasoning and coding) within a leaderboard framework. Our goal is to address two core questions: (1) How do we derive more accurate domain-specific scores by borrowing information across domains? and (2) How do we define and estimate an overall score that aggregates performance across multiple domains? To solve these problems, we propose a novel statistical framework based on representation Multi-task Learning (MTL) and an item response theory model. Specifically, we define overall and domain-specific LLM traits through an Item Response Theory (IRT) model, and propose an MTL approach to estimate these traits from item-level response data. We develop a computationally efficient estimator and establish its minimax optimality under certain asymptotic regimes. This framework provides a rigorous measurement foundation for systematic LLM evaluation. We conduct extensive simulations, demonstrating the superior performance of the proposed method over competing methods. Crucially for the Applications and Case Studies section, we apply the proposed framework to MMLU response data from the Hugging Face Open LLM Leaderboard, covering 4,272 LLMs and 13,232 items across 56 subjects. The empirical analysis reveals substantial heterogeneity in domain size and difficulty, together with strong positive cross-domain dependence, highlighting the practical value and substantive insights generated by our approach.

Robust Causal Inference for EHR-based Studies of Point Exposures with Missingness in Eligibility Criteria

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2504.16230v4 Announce Type: replace-cross Abstract: Missingness in variables that define study eligibility criteria is a seldom addressed challenge in electronic health record (EHR)-based settings. Patients with incomplete eligibility information are typically excluded from analysis without consideration of the (implicit) assumptions being made, leaving study conclusions subject to potential selection bias. In an effort to ascertain eligibility for more patients, researchers may look back further in time prior to study baseline, inappropriately including individuals who, unbeknownst to the researcher, would fail to meet eligibility at baseline. To the best of our knowledge, however, little work has been done to mitigate these concerns. We propose a robust and efficient estimator of the causal average treatment effect on the treated, defined in the study-eligible population, where eligibility-defining covariates are missing at random. The approach facilitates flexible machine-learning strategies for component nuisance functions while maintaining valid asymptotic inference. This method is applied to EHR data from Kaiser Permanente on 14,809 patients undergoing bariatric surgery, comparing two surgical interventions for long-term weight and glycemic outcomes among severely obese patients with type II diabetes mellitus. Our results confirm a weight-loss advantage for Roux-en-Y gastric bypass over sleeve gastrectomy, but are less suggestive of a diabetes remission advantage than complete-case analyses indicate.

postshock: An R Package for Donor-Adjusted Forecasting After Structural Shocks

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11841v1 Announce Type: new Abstract: We present the postshock R package, which implements and extends a donor-based framework for forecasting when a structural shock is known and the target response of interest is not yet observed. The package estimates shock effects from historical donor episodes, balances donors using specified matching features, and transfers the resulting adjustment to a target-series forecast. It provides integrated workflows for conditional mean forecasting through ARIMA and ARIMAX models and conditional variance forecasting through GARCH-X models. Additional functionality includes structured donor pools, control-shock regressors, automated GARCH-X order selection, processed data objects, and reproducible empirical workflows.

Bayesian Estimation of Continuous Brain Connectivity with Log-Gaussian Cox Processes

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11250v1 Announce Type: cross Abstract: Continuous structural connectivity describes the connection between any two points of the cortical surface by an intensity function. Based on the endpoints of tractography streamlines, existing methods estimate this function mostly by kernel smoothing, which only gives a point estimate. We propose a Bayesian framework that estimates continuous connectivity with uncertainty quantification. The endpoints of tractography streamlines, mapped to two spheres, are modeled by a log-Gaussian Cox process on the product of the spheres with a Mat\'ern Gaussian process prior. With the finite element representation of the prior, the Laplace approximation of the posterior enables the computation on a fine mesh with over 400,000 latent variables per hemisphere pair. Numerical experiments show the accuracy of the point estimate of this approach and the coverage of its credible intervals. In the Adolescent Brain Cognitive Development Study, the proposed method predicts held-out streamlines better than kernel smoothing.

Regularized Small Area Estimation with Graph Laplacian Benchmarking priors

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11266v1 Announce Type: cross Abstract: Small area estimation (SAE) often requires both borrowing information across areas and benchmarking estimates to reliable aggregates. We develop a Bayesian framework that addresses these two objectives jointly through a new family of Benchmarking priors. The priors are induced by a benchmark-constrained regularization problem. The resulting family includes a Benchmarking Prior that incorporates the benchmarking restrictions without additional regularization across areas, and Single and Multi-View Laplacian Benchmarking Priors that introduce regularization through graph Laplacians constructed from area similarities based on external covariate information. For posterior computation under these degenerate priors, we develop tailored MCMC algorithms based on a reduced parameterization of the constraint space. We assess the proposed models using a data-based simulation and apply the framework to estimate Average Household Size (AHS) at the municipality level in Colombia in 2025. In this application, graph-based regularization improves model performance, with the Multi-View models generally producing more precise municipality-level estimates.

Bayesian Soft-Tree Poisson Process Model for Covariate-Dependent Point Patterns

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11343v1 Announce Type: cross Abstract: Estimating covariate-dependent intensity functions from spatial point pattern is challenging when the integrated intensity function cannot be evaluated analytically. This challenge becomes even worse in Bayesian inference due to repeated integration of the intensity function over the high-dimensional covariate space. This paper develops a Bayesian soft-tree Poisson process model that combines adaptive covariate partitioning with smooth intensity function. The key idea is to use soft gating functions to smooth transitions between partition boundaries in a tree generating process while preserving analytic evaluation of integrated intensity. A Bayesian CART prior is adopted to learn the partition structure from data. Given the partition tree, conjugate priors are assigned on leaf parameters to enable analytic marginal likelihood computation. This paper also develops a reversible-jump Markov chain Monte Carlo (RJ-MCMC) algorithm for posterior inference. Posterior consistency is established for the proposed model with respect to the Hellinger distance. Extensive simulation studies and an application to wildfire data confirm the advantages of the proposed method over existing methods.

NExt-LMM: a two-stage LMM framework with near-exact variance components for genome-wide association studies

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2508.05278v2 Announce Type: replace Abstract: Linear mixed models (LMMs) are widely used in genome-wide association studies (GWAS) to account for population stratification and cryptic relatedness. However, their practical application remains computationally challenging because parameter estimation and association testing require large-scale operations on genetic similarity matrices (GSMs). Here, we present NExt-LMM, a two-stage framework for scalable LMM-based GWAS. In the first stage, NExt-LMM obtains a preliminary estimate of a shared variance ratio under the null model. In the second stage, it constructs the corresponding covariance matrix and accelerates downstream inference through a Hierarchical Off-Diagonal Low-Rank (HODLR) representation. Specifically, NExt-LMM exploits the low-rank structure of off-diagonal covariance blocks to enable substantially faster matrix factorization and inverse-related computations than conventional dense decompositions. It then reuses the resulting HODLR-based covariance representation to accelerate maximum-likelihood-based inference under the shared variance-ratio setting. We further establish error bounds that account for both sources of approximation in the framework: the preliminary variance-ratio estimate and the HODLR approximation. In particular, we show that, conditional on a fixed variance ratio, the NExt-LMM estimator can be made arbitrarily close to the exact shared-variance estimator as the matrix approximation tolerance approaches zero. \AAA{Numerical experiments show that NExt-LMM improves computational efficiency while maintaining high accuracy relative to existing methods, and that the size of this improvement is governed by the numerical rank retained at the tolerance required for calibrated association inference.} We provide an open-source Python implementation at https://github.com/ZhibinPU/NExt-LMM.

On the Convergence of Wasserstein Gradient Descent for Sampling

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2602.03413v2 Announce Type: replace Abstract: This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the Wasserstein space for which the WGD scheme is guaranteed to converge, thereby providing new theoretical foundations for optimization-based sampling methods on measure spaces. For practical implementation, we construct a particle-based WGD algorithm in which the score function is estimated via score matching. Through a series of numerical experiments, we demonstrate that WGD can provide good approximation to a variety of complex target distributions, including those that pose substantial challenges for standard MCMC and parametric variational Bayes methods. These results suggest that WGD offers a promising and flexible alternative for scalable Bayesian inference in high-dimensional or multimodal settings.

Treatment Effect Modification by Latent Classes

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10851v1 Announce Type: new Abstract: Many treatments have effects that plausibly vary by latent classes. For example, the effect of personalized video recommendations may be stronger for users who seek a new discovery than for users seeking to rewatch something familiar. In the context of user journeys on digital platforms, we can conceptualize user moods as dynamic latent states that lead to distinct action distributions. Because mood is unobserved, we infer it from a user's pre-treatment actions using a hidden Markov model (HMM), and then leverage the latent state as an interpretable treatment effect modifier when evaluating experiment results. Under a treatment-effect sufficiency assumption, each observable conditional effect is a known mixture of the latent effects, so state-specific effects are identified when state posteriors are sufficiently heterogeneous. We propose an estimator that is Neyman-orthogonal to errors in the fitted HMM, enabling standard influence-function confidence intervals. In a real-world large-scale A/B test of a new recommendation model at Netflix, our latent-state analysis reveals that heavy-engagement users show significantly positive effects across all treatment variants, with limited evidence of benefit among less-active and rewatch-oriented users.

Hypothesis Testing for Nonlinear and Interactive Effects Using Additive Gaussian Processes

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10907v1 Announce Type: new Abstract: Real-world data often exhibit nonlinear, interactive associations between predictors and an outcome. For example, in public health studies, environmental exposures and demographic variables can have nonlinear associations with health outcomes and modify the associations of other predictors. Parametric regression models facilitate interpretable inference and hypothesis testing with Type I error rate control, but may be misspecified when associations are nonlinear. In contrast, flexible nonparametric regression models such as Gaussian processes (GPs) can capture complex nonlinearity, but are often more difficult to interpret and do not readily provide hypothesis tests with Type I error rate control. To bridge this gap, we propose a hypothesis testing framework based on additive GPs restricted to pairwise interactions, allowing tests of variable associations and interaction effects with Type I error rate control. We further establish contraction rates for additive GPs, providing theoretical support for their reduced dependence on predictor dimension when higher-order interactions are absent. Through simulations, we show that restricting the model to pairwise interactions can substantially improve testing power relative to methods based on standard GPs. Applications to environmental health studies identify nonlinear associations between metal exposures and health outcomes as well as effect modification by demographic factors.

Bayesian inference under model misspecification

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11173v1 Announce Type: new Abstract: The likelihood input to a Bayesian analysis almost never exactly represents how the data were generated, calling into question the validity of posterior inferences. We review a variational interpretation of the Bayesian posterior as an alternative justification for its use under model misspecification, and consider the resulting implications on uncertainty quantification and parameter estimation. We then introduce a range of techniques that seek to obtain generalised Bayesian inferences that account for model misspecification

Improved E-Value Thresholds with Applications to Multiple and Sequential Testing

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11186v1 Announce Type: new Abstract: E-values provide a flexible framework for statistical inference, but the universal threshold $1/\alpha$ can be conservative when the null distribution has additional structure. We study how structural restrictions limit the worst-case concentration underlying Markov's inequality, using a nondecreasing density model to constrain tail allocation and an $L$-Lipschitz density model to control local concentration. The nondecreasing model gives the minimax rejection threshold, and the Lipschitz condition yields a sharper closed-form threshold with an $O(L^{-1/2})$ relative improvement over $1/\alpha$. We further show that this threshold is asymptotically sharp as $\alpha\to0$, in the sense that no uniformly valid threshold can improve on it by a fixed positive $L$-dependent amount. We then incorporate the Lipschitz calibration into multiple testing procedures with FDR control and use the same structural information to construct calibrated conditional e-values for anytime-valid sequential inference. Numerical experiments illustrate the resulting gains in discoveries and the trade-offs of the sequential procedures.

A Semiparametric Functional Generalized Linear Model for Multi-Population Data

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11208v1 Announce Type: new Abstract: Functional generalized linear models provide a flexible framework for relating a scalar response to functional and scalar predictors, but their conventional formulation requires specification of the response distribution and is typically developed for a single population. We propose a semiparametric functional generalized linear model for multi-population data that leaves the baseline response distributions unspecified and links them across populations through a density ratio model. The proposed framework accommodates both functional and scalar predictors while borrowing information across related populations. We develop a maximum empirical likelihood estimation procedure and use penalized B-spline approximations to estimate the functional coefficients. A cross-validation procedure based on a kernel-smoothed empirical likelihood density estimator is introduced to select the smoothing parameters. Simulation studies show that borrowing information through the density ratio structure can improve estimation efficiency relative to fitting each population separately, and that the proposed semiparametric method remains competitive when a parametric Gaussian model is correctly specified while providing substantial robustness when it is misspecified. We illustrate the method using county-level soybean yield data from Kansas, with daily temperature curves and irrigation levels as predictors.

High-Dimensional Two-Sample Covariance Testing with Null-Preserving Transformations

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11249v1 Announce Type: new Abstract: Testing equality of two high-dimensional covariance matrices is challenging when many entries differ only slightly. Dependence among sample covariance entries can also affect the finite-sample size and power of tests that aggregate their differences. We propose a studentized $\ell_2$-type statistic that averages squared, marginally standardized differences between corresponding entries of the two sample covariance matrices. Before constructing the statistic, we apply the same nonsingular linear transformation to both samples. In the transformed coordinates, the covariance-equality hypothesis is unchanged, whereas the standardized differences and correlations among their estimators generally change. The transformation can therefore incorporate structural or scientific information without reducing dimension. We approximate the null distribution using a Gaussian multiplier bootstrap that uses coordinatewise studentization and avoids forming or inverting the full covariance matrix of the vectorized sample covariance entries. For deterministic transformations, we derive nonasymptotic Gaussian and bootstrap approximation bounds and establish asymptotic size validity and power consistency. We also show that replacing a population transformation by a same-sample estimator leaves the statistic and bootstrap critical value asymptotically unchanged in relative terms under an operator-norm convergence condition. Simulations show that suitable transformations improve size accuracy and power under weak dependence. An analysis of breast cancer gene-expression data illustrates the method.

FissionGuard: Testing Local Watermark Proportions with FDR Control

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11625v1 Announce Type: new Abstract: A watermark detector can flag a text even when only a small fraction of its tokens are watermarked. We study sequential auditing to identify local passages whose watermark proportions exceed a prespecified threshold. Each alarm fixes a candidate passage's endpoint, while its start is chosen from earlier tokens. Reusing the same evidence to locate and test a passage can invalidate inference. We propose FissionGuard, which uses data fission to construct an alarm value and a validation value from each token-level $p$-value. The alarm values guide alarms and localization. The validation values yield passage-level $p$-values through partial conjunction, excluding as many of the strongest signals as the proportion null allows. These $p$-values are used to test the corresponding hypotheses at levels assigned by an online multiple-testing procedure. Under the stated watermark generation model, allowing dependence among token-level $p$-values at watermarked positions, we prove finite-sample false discovery rate (FDR) control among reported passages at every fixed finite horizon. We also derive a finite-sample lower bound on power for testing nonnull candidates. Experiments on synthetic streams and Mistral and Qwen generations across four marking layouts show gains in watermarked-token coverage over sample splitting, with empirical FDR below the target.

Manifold Regression

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11828v1 Announce Type: new Abstract: Conventional statistical modeling typically assumes a one-to-one mapping between input and output variables, where one-to-one is used in the predictive sense that a specified input results in a unique output. Many scientific and engineering systems, however, exhibit non-one-to-one(noto) input-output relations. In a noto relation, the same input may correspond to multiple admissible outputs, so the conventional statistical models may not be appropriate. This paper develops manifold regression, a parametric modeling framework for such noto input-output relations, which represents the underlying input-output relation through a latent manifold. The manifold is specified upto an unknown finite dimensional parameter and we estimate the unknown parameters from ordinary input-output observations by regularized profile optimization with a robust solver. Once the manifold has been learned, prediction is obtained by slicing the estimated manifold along a specified coordinate value. Because a slice may contain multiple latent roots, the resulting manifold prediction is naturally set-valued. This formulation extends predictive learning beyond conventional one-to-one statistical models while containing classical regression and inverse prediction as special cases. Theoretical results are established to justify the manifold regression model and its sliced prediction sets; and case studies are used to demonstrate stable performance across representative noto cases.

Nonparametric covariance estimation with bias correction for spatial lattice processes

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11860v1 Announce Type: new Abstract: Accurate covariance estimation is crucial for spatial data analysis. While parametric methods can suffer from model misspecification leading to wrong conclusions, nonparametric approaches are often neglected in practice as they rely on the estimation of a large number of covariance parameters and often face finite-sample bias issues. In this paper, we study the bias properties of sample covariance estimators for stationary lattice processes on $\mathbb{Z}^2$, when the true mean parameter is unknown and has to be estimated. We derive exact formulas for the finite-sample biases of sample covariance estimators and show that their expectations are linear combinations of population covariances determined by spatial lag and sample size. Based on this characterization, we propose jointly bias-corrected covariance estimators that are nearly unbiased. Additionally, we derive formulas for the mean-squared error and prove asymptotic normality results that show asymptotic equivalence for the estimators with and without bias correction. Simulations demonstrate substantial reductions of bias and often also in terms of MSE, particularly under strong spatial dependence. A kriging application to topography data further illustrates the practical benefits of the proposed approach.

Re-randomization-probability weighting for population-adjusted comparisons of maintenance outcomes across trial designs

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12074v1 Announce Type: new Abstract: Randomized-withdrawal trials re-randomize induction responders to continued treatment or withdrawal. Baseline characteristics are often reported for the induction population but unavailable for responders, limiting population-adjusted indirect comparisons of maintenance outcomes. We describe re-randomization-probability weighting, which combines induction-population calibration with inverse weighting by known maintenance assignment probabilities. Coding induction non-response as failure defines durable response: response at both induction and maintenance. The design weights reproduce induction-population covariate totals in randomization expectation, allowing population adjustment using reported induction baselines. Conditional maintenance probabilities can also be estimated, although different induction treatments generate different responder populations. A synthetic three-trial demonstration reduced durable-response bias from 0.106 to 0.001 and from 0.055 to 0.001 in two comparisons. Full-procedure simulations showed interval coverage of 91.5% - 94.3%; stress scenarios illustrated bias from omitted covariates and incorrect assignment weights. The method connects established design weighting and aggregate dilution approaches to population-adjusted comparison across randomized-withdrawal and treat-through designs. It requires compatible durable-response endpoints and credible transport and modeling assumptions. Withdrawal after different induction regimens is not automatically a common comparator. Where no valid anchor exists, unanchored comparison is appropriate only if its demanding adjustment assumptions are defensible.

Robust variance estimation for multiple imputation using predictive mean matching or parametric imputation models

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12215v1 Announce Type: new Abstract: Multiple imputation (MI) is widely used for handling missing data in medical research, with variance commonly estimated using Rubin's rules (RR). RR is simple to apply, but under uncongeniality between the imputation and analysis procedures, its variance estimate can be either too small or too large, leading to miscalibrated confidence intervals. Robins and Wang (RW) developed an estimating-equation variance estimator that does not require congeniality under the conditions of their parametric imputation framework. Practical use of RW, however, has been limited by the lack of accessible software and by the additional variance calculations required for modern imputation workflows. We develop an R package, rw, construct RW variance components for normal and logistic conditional imputation models fitted through mice, and propose an approximate RW variance procedure for predictive mean matching (PMM). The PMM procedure preserves the original imputations and selected donors. For the variance calculation, we define differentiable donor probabilities and use expected analysis scores to approximate the cross-moment between analysis and imputation scores. Analysis scores are summed by recorded donor to account for donor reuse. We evaluate the proposed methods in benchmark simulations based on the original RW setting and in validation-study simulations motivated by electronic health record data. RR coverage was up to approximately 23 percentage points below the nominal 95% level in some settings and above nominal in others. The proposed RW estimators generally produced coverage closer to the nominal level in larger samples under both parametric and PMM imputation, while retaining the same completed-data point estimates as RR.

Data generation for the logistic regression model under controlled conditions

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12381v1 Announce Type: new Abstract: Generating data with desired properties for a logistic regression model under controlled conditions is challenging. We propose an integrated iterative bisection algorithm that determines values of the intercept and regression coefficients capable of generating data with a specified prevalence and predictive accuracy. The performance of the proposed method is demonstrated through simulation studies. We further show that the choice of parameter values, or, in a Bayesian setting, the choice of priors for these parameters, induces a particular level of predictive accuracy. This relationship should therefore be taken into account when generating data for model evaluation under controlled conditions.

Certified Corruption Budgets: Anytime-Valid Leaderboard Claims under Adaptive Rigging

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10597v1 Announce Type: cross Abstract: Public leaderboards for AI models are read continuously, and attackers can see every published standing. Vote rigging, selective disclosure of private variants, and benchmark contamination can each move a ranking. Existing guarantees assume genuine records or bound the corruption per step, which an attacker who corrupts in bursts evades. We introduce the certified corruption budget, a tolerance $\widehat{B}_t$ computed after $t$ records and published with each pairwise claim. With probability at least $1-\alpha$, simultaneously at all times, the claim is correct or more than $\widehat{B}_t$ records were corrupted. It holds against attackers who watch every certificate, with no bound on their budget. Forged records and records altered once seen require different certificates: the certificate for forgeries fails, with probability approaching one, against an attacker who flips votes it has seen, while one that charges roughly twice as much per record remains valid, with constant bets even against attackers who see the future, and no smaller charge is valid at every level. The certified budget grows nearly as fast as any valid method allows: with a win fraction $\frac{1}{2}+\delta$, each new record adds close to $2\delta$ to the number of forged records the claim can withstand ($\delta$ flipped). Publishing the best of $V$ private variants costs only an amount growing like $\log V$. In replays on 1.8 million Chatbot Arena votes, a few hundred rigged votes make standard confidence intervals certify false orderings, while ours stays valid. On real votes, our certificate shows that clearly separated models withstand about 2,000 forged votes.

D-SLR: The Disjoint Row-Sparse plus Low-Rank Decomposition

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10636v1 Announce Type: cross Abstract: Compressing a matrix for reconstruction still defaults to the truncated SVD, approximating the data with a single low-rank structure. It is common to reduce the residual further by adding an overlapping row-sparse component, but methods that solve this joint problem often require iterative solvers and tuning of regularization parameters. We propose the Disjoint Row-Sparse plus Low-Rank (D-SLR) decomposition, a closed-form drop-in for the truncated SVD that improves or exactly matches it. D-SLR restricts rows to either being stored verbatim or approximated by the low-rank fit, never both. Under squared error this restriction costs nothing: the joint optimum is attainable disjointly with fewer parameters at every non-trivial rank and stored row count (shape). With zero stored rows D-SLR reduces to the truncated SVD, so it never does worse at equal cost. The algorithm scores the entire error-versus-parameters tradeoff, and the solution is chosen afterwards by a supplied error target or parameter count, or by a selection rule. The grid and solution together cost three SVDs, with no tuning or regularization. We derive an assumption-free, a-posteriori lower bound on the error at every shape, giving each solution a computable certificate on the potential gain of any other choice of rank and stored rows. Experiments on synthetic and real data (LLM embedding tables, network traffic, hyperspectral images) confirm the gains and quantify the certificate.

Transformed Samplers with Variance Reduction

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10870v1 Announce Type: cross Abstract: Markov chain Monte Carlo (MCMC) methods are the standard tool for computing expectations under complex probability distributions. Control variates reduce the variance of the resulting estimates, but a good control variate requires solving the Poisson equation of the sampler, which rarely admits a closed-form solution. Exact solutions are available when the sampler's kernel has a known spectral decomposition on a simple reference density. In our work, we extend these solutions to general targets through a learned change of variables. A bijection, such as a normalizing flow, is trained so that the target becomes close to the reference in a latent space, and we show that Markov kernels and their Poisson solutions are transformed by any bijection. Running such samplers in the latent space then yields explicit control variates, and the estimator is consistent under mild tail conditions on the map and target. Importance sampling (IS) from the flow is the limiting case of the same construction and the control variates apply to it as well. Experiments on synthetic targets and real posteriors compare the procedure against state-of-the-art samplers and control variates.

How to post-train on a surrogate: Envelope sampling mitigates reward hacking

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11281v1 Announce Type: cross Abstract: Large language models (LLMs) are commonly post-trained against LLM judges and other cheap surrogates because the true reward, such as human preference, is too expensive to query at scale. This practice often leads to reward hacking, where reinforcement learning against a miscalibrated surrogate leads to undesirable side effects. In this work, we study a setting in which a small number $n$ of model outputs are annotated with ground-truth labels (e.g., from expert review) and used to recalibrate the LLM judge before optimizing against it. Prior approaches to judge recalibration are costly or heuristic, and it is known that on-policy sampling fails when the surrogate is miscalibrated on a rare set of outputs. In this work, we propose envelope sampling, a theoretically-grounded method for judge recalibration that seeks to minimize an upper bound on the regret of the post-trained model under the assumption that the human reward and re-calibrated reward lie in an $L^2$ ball around the judge. We give practical algorithms to sample from the envelope by rejection or by fine-tuning against a modified reward, and experiments on clinical note generation and on a controlled sycophancy task show that recalibrating on envelope samples mitigates reward hacking where recalibrating on base-model samples does not.

Sample-Efficient Generative Conformal Prediction

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11349v1 Announce Type: cross Abstract: Generative conformal prediction builds uncertainty sets from samples of a conditional generator, which are efficient only when the samples represent the response distribution well. This can require many samples, each of which can be costly, as in large diffusion models and scientific simulators, so the sampling budget must be used efficiently. Existing methods draw the same number of samples at every input, wasting samples where the response distribution is simple and undersampling where it is complex, which inflates sets and leaves those inputs under-covered. We propose CASA (Conformal Adaptive Sample Allocation), which characterizes the marginal value of an additional sample and allocates samples across inputs to minimize the expected set size subject to marginal coverage and an average sampling budget. Theoretical analysis shows that adaptive allocation yields smaller sets than a fixed count at the same budget: a missed mode forces a radius that spans the gap between modes, and even oracle radius cannot compensate for it. On synthetic and real tasks, CASA produces substantially smaller sets at the same budget, often improves conditional coverage, and complements existing radius-adaptive methods.

Estimating great expectations under autoregressive language models with potentials

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11399v1 Announce Type: cross Abstract: Many applications of language models hinge not on individual samples but on the expectation of a test functional under the model. Estimating such expectations reliably can be computationally expensive. In this paper, we show how to make estimation more efficient by exploiting the next-token conditional probabilities which are available as a by-product of sampling. We do so through potentials: real-valued functions on prefixes that decompose the test functional additively. We construct an estimator whose variance depends on the chosen potential, and derive conditions under which a potential reduces this variance. We then develop practical potentials for several estimands and applications, and demonstrate substantial variance reductions across several estimands at comparable computational cost.

Feature Space Adaptation for Effortless Gaussian Process Flows

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11459v1 Announce Type: cross Abstract: Outside the linear-Gaussian regime, conditional sampling from Gaussian processes (GPs) is challenging. Recent methods such as FlowGP (Moss et al., (2026)) can condition on arbitrary non-linear and non-Gaussian statements, but at considerable cost: an expensive iterative and high-dimensional diffusion that requires hand-specified kernel hyperparameters. In this paper, we alleviate two significant drawbacks of FlowGP by (1) introducing kernel approximations that enable scaling to high-resolution domains and (2) proposing a way to obtain the marginal likelihood by measuring the work needed to steer the diffusion towards conditioning statements. We enable, for the first time, hyperparameter optimisation within FlowGP and demonstrate our approach on probabilistic downscaling from areal summary statistics, PDE solution inference on irregular domains, and recovery of sea level anomaly fields from non-Gaussian satellite observations.

Anytime-valid detection of LLM weight exfiltration

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11843v1 Announce Type: cross Abstract: A compromised LLM inference server can leak model weights by encoding payload bits in otherwise plausible token choices. A replay of the same prompt in a trusted server can expose such deviations, but benign numerical nondeterminism also causes token mismatches. Patient attackers can therefore hide within normal variation unless evidence is combined across responses. We introduce a prompt-level e-process that calibrates whole-response mismatch events on trusted benign traffic and accumulates evidence sequentially while, under a calibration-transfer assumption, controlling the probability of any false alarm over an unbounded monitoring horizon. We evaluate it on four models against a seed-blind attack and a stronger seed-aware attack that hides payload bits only in near-ties to remain stealthy, analyzing the channel capacity vs detectability trade-off. Compared with a hard per-token alarm, the e-process combines weak evidence across responses while providing explicit anytime false-alarm control.

Consistent intercept estimation and inference for unit-root INAR(2) processes

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2609.23339v2 Announce Type: replace Abstract: \citet{barczy2014asymptotic} showed that the ordinary least-squares (OLS) estimator of the innovation mean is inconsistent for a unit-root INAR(2) process. We construct a consistent intercept estimator using inverse-time weighted least squares (WLS) and derive its mixed-rate asymptotics: the intercept estimator is asymptotically normal at rate $\sqrt{\log n}$, with a Gaussian limit independent of the autoregressive limits, while the autoregressive estimators retain their OLS rates. We develop an OLS unit-root test calibrated with WLS nuisance estimates. Under the maintained unit root, residual-score Gaussian intervals for the innovation mean and long-run drift remain asymptotically valid after test nonrejection. Simulations show that WLS reduces root mean squared error for both quantities relative to OLS, with further gains from imposing the unit root. An application to two Canadian flood inventories shows that conclusions about persistence depend on the inventory and weighting offset.

Lambda-quantiles under the microscope

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2608.07122v2 Announce Type: replace Abstract: We study Lambda-quantiles, a generalisation of classical quantiles in which the constant probability level $\lambda \in [0,1]$ is replaced by a functional parameter $\Lambda \colon \mathbb{R} \to [0,1]$. We consider the general case of non-monotone $\Lambda$, which arises naturally if closure properties of the class of corresponding Lambda-quantiles with respect to inf-aggregation or with respect to mixtures are required. As preliminary results, we characterise finiteness, constancy, and what we call the attainment property known from classical quantiles. We then consider the problem of reconstructing $\Lambda$ from the values of $\Lambda$-quantiles on a suitable family of simple distributions, showing its identifiability under mild assumptions. Next, we substantially refine several results obtained in the literature on weak upper and lower semicontinuity and on the property of convexity of the level sets with respect to mixtures, obtaining in both cases almost complete characterisations without any monotonicity assumption. We then move to the case in which $\Lambda$ has bounded variation, which enables us to prove a mixture representation result: any such $\Lambda$-quantile can be rewritten as a Lambda-quantile with an increasing functional parameter, evaluated at a mixture of the original distribution with a fixed reference distribution at a fixed weight, thus reducing the complexity of the parameter from bounded variation to monotone. Finally, we introduce and study the notion of the ordinal covariance group of a risk measure, showing that in the case of a $\Lambda$-quantile it coincides with the compositional invariance group of $\Lambda$ and with a certain group of measure-preserving transformations of the signed measure associated with $\Lambda$.

Estimation of the sub-Gaussian Parameter

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2606.06384v2 Announce Type: replace Abstract: The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $\xi^2_\star = \sup_{\lambda \in \mathbb{R}} L(\lambda)$ where $L(\lambda) = \frac{2}{\lambda^2} \log \mathbb{E} e^{\lambda X}$ is a weighted cumulant generating function. We study the estimation of $\xi^2_\star$ and prove that the minimax risk is governed by a non-increasing function $\delta_P(C) = \sup_{|\lambda| \geq C} L(\lambda) - \sup_{|\lambda| \leq C} L(\lambda)$ which captures the influence of the tail behavior of the distribution $P$. Over the class of distributions with $\delta_P \leq r$ for a non-increasing function $r$, the minimax risk is, up to a multiplicative constant, lower bounded by $r(\sqrt{\log n}) + n^{-1/2}$ and upper bounded by $r((\log n)^{1/2-\varepsilon}) + n^{-1/2 + \varepsilon}$ for any $\varepsilon > 0$. Our estimator for the upper bound is based on constrained maximization of the empirical analogue of $L$. In addition to being almost minimax optimal and adaptive, we further prove that the estimator is asymptotic normal under suitable conditions and that, if the underlying distribution is not sub-Gaussian, the estimator diverges with a rate determined by the heaviness of the distributional tail.

Handling Covariate Mismatch in Collaborative Linear Prediction

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2602.02083v2 Announce Type: replace Abstract: Training predictive models across multiple centers typically assumes that all centers collect the same set of covariates. In practice, however, they may record different features of their observations, a setting we refer to as covariate mismatch. We study linear prediction under this challenging setting, assuming center-wise MCAR missingness patterns, and develop estimators that exploit information across centers despite heterogeneous feature sets. In the low-dimensional regime, we propose a plug-in estimator of the oracle linear predictor based on component-wise aggregation of covariance and cross-moment estimates. In higher dimensions, we study an impute-then-regress strategy that first completes the missing covariates using an exchangeability-preserving imputation procedure and then fits a ridge-regularized linear model. All proposed estimators are compatible with federated learning constraints: individual-level data remain local to each center, and only aggregated quantities are exchanged. We provide asymptotic and finite-sample learning rates for our predictors, explicitly characterizing their behaviour with the global dimension, the center-specific feature partition, and the distribution of samples across centers, and validate our approach through numerical experiments.

Efficient quadratic entropy with distance sketches

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11976v1 Announce Type: cross Abstract: We detail scalable methods for approximating the quadratic entropy $p^T d p$ for arbitrary distributions $p$ and common distances $d$ of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where $d$ is held constant while $p$ varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.

Dense uniqueness and dense nonuniqueness of Fr\'echet means

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11946v1 Announce Type: cross Abstract: From previous results it follows that probability distributions on metric spaces featuring unique Fr\'echet means are dense among measures admitting means in both the quadratic Wasserstein metric and the total variation metric. Additionally, we show that the converse also holds on complete finite-dimensional noncontractible Alexandrov spaces with curvatures bounded from below, which encompass compact manifolds without boundaries and nonmanifold shape spaces: Probability distributions featuring nonunique Fr\'echet means are also dense in both the Wasserstein metric and the total variation metric. Moreover, in either metric, no nonempty open set of probability measures admits a continuous selection of means. This sharpens a previous result on zero reach of the Dirac embedding. Our argument combines cut-locus avoidance for atoms with a topological obstruction. For Riemannian manifolds, all of our conclusions hold for all exponents $1 < p < \infty$, also.

RobustLDS: Learning linear dynamical systems under adversarial corruptions

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11906v1 Announce Type: cross Abstract: We consider the problem of learning linear dynamical systems under adversarial contamination from a single trajectory of length $T$. While identification of linear dynamical systems itself is well-studied, the problem of robust system identification under adversarial contamination is relatively less explored. In this work, we study the setting where a fraction of the $T$ observations are contaminated by adversarial outliers. We propose different estimators based on relaxations of least-trimmed squares along with an alternating minimization algorithm. Furthermore, we also propose two estimators which exploit the group-sparsity (through penalization/hard-constraints) of the outliers. For the estimator with group-sparse penalty, we derive non-asymptotic error bounds which establish its robustness to outliers. We also show empirically that the proposed estimators work well in practice.

Learning structured linear dynamical systems from missing observations

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11869v1 Announce Type: cross Abstract: We consider the problem of learning structured linear dynamical systems over convex sets $\mathcal{K}$, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of $\mathcal{K}$, the trajectory length $T$, and the sub-sampling probability $p$. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) $\mathcal{K}$ is a subspace, (ii) $\mathcal{K}$ is the set of bi-isotonic matrices, and (iii) $\mathcal{K}$ is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of $T$ much smaller than what is required in the unconstrained case, and for $p = o(1)$.

Conditional Kernel Stein Discrepancy

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11863v1 Announce Type: cross Abstract: Kernel Stein discrepancies (KSDs) provide a versatile tool for comparing distributions. One of their main applications is in quantifying the goodness-of-fit (GoF) between a data-generating distribution and a prescribed target distribution. In this work, we study the related problem of conditional GoF quantification: given only a (possibly non-normalized) conditional target model, without information on the distribution of its covariates, and samples from a joint distribution, the goal is to assess how well the conditional distribution of the samples matches the target. To tackle this setting, we present a framework that allows lifting unconditional KSDs to the conditional setting through an operator-valued kernel on the covariate space, going beyond the known Euclidean case. We establish that our suggested statistic vanishes if and only if the conditional model and the true conditional distribution agree for almost all covariates and deploy it to test conditional GoF on smooth manifolds and on discrete spaces. Our experiments on level, power, and runtime demonstrate the viability of testing on these domains using the proposed statistic.

Anchored multiple testing: a transparent use of e-closure to improve FDR procedures

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11279v1 Announce Type: cross Abstract: The recent e-closure method can recover every procedure that controls FDR (and other expectation losses). But the recovered e-collection is ``self-referential'' and gives no insight on how to improve the procedure (if improvable), and some recent improvements have been somewhat opaque. We introduce an elementary new technique called anchoring that exploits looseness in existing FDR proofs to enlarge a baseline multiple-testing procedure's self-referential local e-value. The resulting e-closure thus transparently retains every baseline discovery (and usually adding more) and controlling the false discovery rate under the same conditions as the baseline. To show that this principle is broadly applicable, we use it to improve a large suite of multiple testing procedures: (i) Anchored-BH dominates the Benjamini-Hochberg (BH) procedure under PRDS while being incomparable to Goeman's recent closed-BH, (ii) Anchored-BY dominates the Benjamini-Yekutieli (BY) procedure under arbitrary dependence while being incomparable to closed-BY, (iii) For two-sided Gaussian p-values (under appropriate covariance conditions), Anchored-2BH dominates running BH twice at half the level on two one-sided p-values, (iv) Anchored-dBH dominates dependence-adjusted BH, (v) Anchored e-BH dominates e-BH and is incomparable to closed e-BH, (vi) Anchored SeqStep+ improves the original (including selective and adpative variants) while preserving ordered rejection structures. All of these are accomplished in sorting or quadratic time. The appendix shows how to dominate Shifted-BH (for two-sided arbitrarily correlated Gaussians) and NDBH (under negative dependent p-values).

The optimal information complexity of VC learning

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10600v1 Announce Type: cross Abstract: Steinke and Zakynthinou(2020) introduces the Conditional Mutual Information (CMI) framework of analyzing the information complexity of learning algorithms based on algorithm-dependent information-theoretic quantities. We study one of these quantities, the evaluated Conditional Mutual Information (eCMI). It has been an interesting question whether the optimal PAC guarantee for VC classes can be recovered from the algorithm-dependent analyses via CMI. And we show that it is possible to recover this guarantee by constructing a learning algorithm whose eCMI is of order O(d) in the realizable case, where d is the VC-dimension of the concept class. Specially, our algorithm is a randomized Majority-of-5 base learners with optimal in-expectation generalization guarantee.

Optimal random quantisers for spherically symmetric distributions

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11772v1 Announce Type: new Abstract: Zador's celebrated theorem is a cornerstone of optimal quantisation: it establishes both the weak limit of the empirical distribution of an optimal $n$-point quantiser in $R^d$ and the decay rate of the associated $L_s$-mean quantisation error. In large dimension, however, observing this asymptotic behaviour requires an astronomically large sample size. We prove that, for spherically symmetric target distributions, optimisation over all spherically symmetric distributions is a convex problem and derive an equivalence theorem that both characterises global optimality and yields a constructive algorithm. We show that, for moderate $n$, random quantisers uniformly distributed on a sphere of suitably chosen radius $R$ perform exceptionally well and, over a broad range of values of $n$, are numerically certified to be optimal among all random quantisers. Their expected distortion has an explicit integral representation that can be evaluated to arbitrary precision, and we prove concentration across random quantisers: the distortion variance tends to zero as $n\to\infty$ for fixed $d$. For $s=2$, both the optimal radius and the associated minimum expected distortion admit exact expressions. For general $s$, the optimal radius can be determined efficiently, and extreme-value theory provides useful approximations when $n$ grows with $d$. Depending on this growth rate, $R$ either converges to zero or approaches a positive limit that is independent of $s$.

Adaptive minimax multivariate $L^1$-deconvolution: harmonic-mean rates under noise filtering, and a $1$-Wasserstein equivalence

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11760v1 Announce Type: new Abstract: We study the multivariate convolution model with additive independent noise, multidimensional signal and noise, aiming to recover the signal's cumulative distribution function from contaminated observations. The noise is ordinary smooth with anisotropic regularity, and the signal belongs to an anisotropic Nikol'skii density class. We extend to the multivariate setting an approximate minimum $L^1$-distance estimator based on integrated kernel density estimation, and establish matching upper and lower bounds for the $L^1$-risk over anisotropic Nikol'skii classes. To our knowledge, this is the first minimax rate, not a sharpening of existing bounds. Although the lower-bound scheme is classical, the test-function construction is novel: it distinguishes no active component from at least one active component. The rate is governed by a censoring mechanism through the positive part, a noise filter in a harmonic-mean representation of the exponent. We further propose a fully data-driven, rate-adaptive procedure selecting an optimal bandwidth vector over the full Nikol'skii scale. On Nikol'skii product density classes, the $L^1$-distance between cumulative distribution functions and the $1$-Wasserstein distance share the same minimax rate, though not equivalent in general, via coordinate-wise decoupling of the $1$-Wasserstein cost on product measures. These findings reveal a link between the two distances, whose full understanding remains an open question.

Single-graph inference for fractal Gaussian networks

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11597v1 Announce Type: new Abstract: We study inference on the strength of Gaussian multiplicative chaos from one geometric graph with unobserved vertex positions. In the planar model, the edge-count statistic has a piecewise deterministic limit with a transition at $\gamma=1$, whereas degree quantiles consistently estimate $\nu=\gamma^2/2$ throughout the subcritical range. Fractional moments give uniform finite-sample risk bounds. At finite resolution, common graph envelopes calibrate tests over continuous parameter boxes with unknown Poisson intensity. They give simultaneous coverage under adaptive refinement for a fixed statistic, and conditional coverage for an independently piloted size--degree residual on a fixed partition. For the exact periodic FFT--pixel approximation, we prove explicit total-variation rates for the annealed spatial Cox law and the observed graph law, uniformly on every compact subcritical range $0\le\gamma\le\Gamma<2$. The rates allow intensity to grow with resolution and imply uniform asymptotic coverage after recalibration at each resolution. Numerical studies examine parameter refinement, residual calibration, and multiresolution stability.

Sequential Conditional Independence Testing with Machine Learning Models

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11388v1 Announce Type: new Abstract: Conditional independence testing is a ubiquitous problem in scientific discovery. The widely employed model-X assumption shifts the modelling burden from the dependence of the output on the inputs to the dependencies within the inputs. Log-optimal e-variables have been studied in this setting, but it remains unclear how to incorporate machine learning models into their design. Other approaches test exchangeability directly, yielding an e-variable with lower power in theory but, surprisingly, higher power in practice. We explain this phenomenon by decomposing the error into null enlargement, approximation, and estimation error. The decomposition shows that GRO e-variable estimates can be beaten because of their worse approximation and estimation errors, and we explore intermediate null hypotheses between model-X conditional independence and exchangeability to reduce these errors. Moreover, the model-X assumption often only holds up to an estimation error, invalidating exact type-I error guarantees. We provide estimation error bounds that accommodate triple robustness results, achieving fast convergence rates.

Decision-Sufficient Posterior Approximation

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11038v1 Announce Type: new Abstract: We investigate the consequences of requiring a posterior approximation to preserve a specified downstream decision problem. A target posterior $P$ and loss determine a regret geometry on actions, a baseline approximation $Q_0$ determines the forward-Kullback-Leibler information required to induce action changes, and a restricted approximation family $\mathcal{Q}$ determines which such changes are available. Contracting KL divergence over Bayes-action fibers gives exact distances to decision adequacy and decision failure together with the least-informative posterior deformations that reach either side of the decision boundary. In regular finite-dimensional problems, the target and baseline constructions have quadratic local limits: a target regret Hessian $G$ and a baseline information metric $J_I$ . Their generalized eigenproblem $Gv = \gamma J_Iv$ orders local decision directions by regret consequence per unit information cost and induces a tolerance-dependent effective dimension. For restricted approximation families, the tangent image separates decision coverage from information efficiency: a family may miss consequential decision directions, or it may realize reachable directions only at excess Fisher cost. The resulting framework provides decision-relative criteria for comparing and designing posterior approximation families.

When Does Inexact Matching Ensure Balance and Inference without Adjustment?

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10873v1 Announce Type: new Abstract: One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments.

On the Impossibility of Estimating the Average Mixing Time

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10860v1 Announce Type: new Abstract: We establish nearly-matching converse bounds on the sample complexity of estimating the average mixing time of a Markov chain from a single stationary trajectory. Unlike the worst-case mixing time, which maximises the total-variation distance to stationarity over all initial states, the average mixing time averages this distance under the stationary distribution and can therefore be substantially smaller. Our converse bounds establish when estimation is impossible, and match the key dependencies in existing achievability bounds, up to logarithmic factors. Together, these bounds provide nearly-tight PAC guarantees for estimating the average mixing time.

Statistical Guarantees for Covariance Estimation with Adversarial Corruption under Constraints

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.10840v1 Announce Type: new Abstract: We obtain a near-minimax rate on covariance estimation of adversarially corrupted Gaussian data in Frobenius norm when the covariance estimation is assumed to lie in a star-shaped set $K \subseteq \mathbb{R}^{n \times n}$. Assuming a known upper bound of $\varepsilon 0} \log \mathrm{M}^{\operatorname{loc}}(\delta, 2c)$, and \begin{align*} \delta^*=\sup\left\{ \delta\geq 0: \frac{N}{\Upsilon^2} \delta^2\leq \log \mathrm{M}_K^{\operatorname{loc}}(\delta,c) \right\} \end{align*} for an arbitrary large constant $c$ and the local metric entropy of $K$, $\mathrm{M}^{\operatorname{loc}}_K(\delta,c)$. We believe this is the first such general result on structured robust covariance estimation in the Frobenius norm.

Testing Algebraic Complete Intersections

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.12288v1 Announce Type: cross Abstract: Given independent and identically distributed samples samples from a probability distribution in a potentially high-dimensional real space, we study the problem of testing whether the distribution is concentrated near a real algebraic complete intersection of prescribed dimension, bounded degree, and bounded condition number. We design an explicit and effective learning procedure which either certifies the nonexistence of such a manifold, up to a controlled relaxation of the approximation threshold, or returns a candidate regression manifold with controlled geometric complexity. Equivalently, the procedure tests the manifold hypothesis within this hypothesis class. The proposed procedure relies on quantitative geometric estimates for regular polynomial systems, which lead to a tractable auxiliary optimization problem. We then develop a data-driven algorithm to solve this auxiliary optimization problem, establishing explicit bounds on its sample and arithmetic complexity.

Automated Detection of Match Phases in Football from Spatio-Temporal Tracking Data Using Graph Neural Networks

Fri, 09 Oct 2026 00:00:00 -0400

arXiv:2610.11571v1 Announce Type: new Abstract: Spatio-temporal tracking data has opened new possibilities for detecting complex tactical patterns in football, yet modeling the interactive movements of multiple players remains challenging. This paper proposes a framework combining graph neural networks (GNNs) with a sequential model to classify match phases on a second-by-second basis across a seven-class taxonomy. Match phase classification is tactically meaningful, and the availability of rule-based labels across 203 matches makes it a suitable testbed for a systematic comparison of adjacency constructions and message-passing layers, a question that has received limited attention in existing research. Our selected GNN-LSTM model outperforms all aggregated-feature baselines, including XGBoost and a Long Short-Term Memory (LSTM) network, as the strongest baseline scores 4.6% lower in macro F1. Graph representations using a domain-informed Delaunay triangulation that approximates passing lanes, paired with a custom Spatial Edge-Augmented Convolution (SEAConv) layer that injects edge attributes directly into messages, achieve the best performance by capturing spatial dependencies while limiting uninformative messages from redundant edges. Integrated Gradients attributions indicate the model uses spatial player configurations, particularly horizontal positioning, in combination with possession and ball-status indicators. This work offers an automated solution for fine-grained tactical analysis, reducing the need for manual tagging and providing deeper insight into dynamic team behavior.

Bayesian Optimization for Dose Finding with Two Agents: Participant Allocation and Final Selection

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09245v1 Announce Type: new Abstract: In two-agent dose-finding trials, the next cohort should help identify a combination for final selection. We studied a constrained knowledge-gradient (cKG) rule with one-cohort lookahead that updates independent Gaussian-process models of efficacy and continuous toxicity, reapplies a probability criterion for mean toxicity, and evaluates the resulting selection. We derived a deterministic calculation over a fixed set of dose combinations, holding fitted model parameters fixed during each hypothetical update. We compared cKG with constrained expected improvement (cEI) and two toxicity-only rules, targeted mean squared error (tMSE) and entropy, in four synthetic scenarios. In the primary obstructive sleep apnea (OSA)-derived scenario, averaged equally over strata and five probability cutoffs, cKG assigned fewer participants to combinations above the true mean-toxicity limit than tMSE (17.92% versus 27.08%), but selected such combinations more often at trial completion (18.80% versus 11.85%). Compared with cEI, cKG had higher mean simulated reduction in the 4%-desaturation apnea-hypopnea index (AHI4) at final selection (7.46 versus 6.72 events/hour), more above-limit final selections (18.80% versus 10.50%), and more above-limit assignments (17.92% versus 15.10%). Across scenarios, its efficacy advantage over cEI was smaller under stricter toxicity criteria. Continuous outcomes, uncalibrated toxicity limits, and a rule that still selects a combination when none meets the criterion limit clinical interpretation. Allocation and final-selection toxicity should be reported separately, alongside efficacy.

A Sensitivity-based Framework for Calibrating Coupled Ordinary Differential Equations under Model Discrepancy

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09261v1 Announce Type: new Abstract: Coupled systems of ordinary differential equations (ODEs) are widely used to model complex physical and biological processes. In these applications, ODE model parameters must be calibrated to field data to enable prediction and parameter inference. In practice, the governing ODEs are an imperfect approximation to the true system, leading to non-negligible model discrepancy that must be incorporated to avoid biased parameter estimates. However, it is well known that highly flexible discrepancy models can confound discrepancy and simulator parameters, leading to poor identifiability. As a result, practitioners often must impose problem-specific prior constraints to adequately regularize the discrepancy, which can be challenging and cumbersome. In this work, we propose a novel calibration framework for coupled, multi-output ODE systems that enforces automatic, model-structural constraints on the discrepancy, improving identifiability without requiring application-specific discrepancy priors. Forward-model gradients are computed via sensitivity equations, solved jointly with the ODE system as a coupled initial value problem. Posterior inference is performed using an adaptive Metropolis-within-Gibbs sampler tailored to the resulting constrained posterior. We demonstrate the approach on three model systems: a mass-spring oscillator, a model of infectious disease spread, and a neuron firing model. We show that our method leads to improved parameter inference and predictive accuracy compared to standard calibration approaches.

An unscented universal filter for joint input-state-parameter estimation of a partially measured system: an application to drive-by structural health monitoring

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09468v1 Announce Type: new Abstract: Drive-by structural health monitoring infers the condition of a bridge from the response of an instrumented vehicle, whose measurements are dominated by the road roughness and the vehicle dynamics. The bridge responses, contact forces and bridge parameters depend on one another through the vehicle-bridge interaction (VBI), so estimating them jointly is desirable. This paper proposes a novel filter in the Universal Filter family, the Unscented Universal Filter (UUF), for joint input-state-parameter estimation of nonlinear systems with unknown inputs. The unknown input is estimated by weighted least squares from the innovation, without any evolution model or statistics, and the system inversion imposes no rank condition on the feedforward matrix. The nonlinear propagation is linearised by the scaled unscented transform, and the linearisation residuals are propagated into the error covariances. For the acceleration-only configuration, auxiliary integrators form pseudo-measurements from the acceleration measurements themselves. The UUF is applied to the coupled VBI system, with the contact forces as the unknown input and the local stiffness of the bridge as the tracked parameter, from the responses of the vehicle body and at most a few bridge responses. In numerical case studies on a simply supported beam and the Old Ada Bridge, a steel truss bridge in Japan, the UUF is compared with classical and state-of-the-art joint estimation filters, all tuned by the same practical strategy. Across the damage severities, locations, road classes and noise levels examined, the UUF yields the lowest total error in most scenarios, and its error varies little with damage severity, location and road class. On the Old Ada Bridge, it identifies the stiffness of a damaged member from acceleration-only measurements, without the suspension parameters of the vehicle, and with a rank-deficient feedforward matrix.

Multivariate LSTM Modeling for Wastewater Quality Prediction

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09996v1 Announce Type: new Abstract: The proposed approach relies on high-frequency multivariate time series collected at the Seine aval (SIAAP 1 ) treatment plant, including pH, temperature, conductivity, and total suspended solids, as well as exogenous variables related to precipitation and measurements from an upstream plant. The objective is to forecast wastewater quality over a 24-hour horizon. A multivariate Long Short-Term Memory (LSTM) recurrent neural network is implemented to capture complex temporal dependencies and nonlinear patterns in the data. The model is trained on one year of data and validated on four months of data (one per season), and is compared with a persistence model and SARIMA models. The evaluation shows an overall superiority of the LSTM model, particularly for variables exhibiting high levels of noise and nonlinearity.

Neutral Is Not Free: Evaluating Downside Risk in Neutral Launches

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10223v1 Announce Type: new Abstract: Evaluating "neutral launches" (e.g., infrastructure upgrades) using traditional confidence interval overlap is flawed: it is dangerously permissive with scarce data and excessively restrictive with abundant data. To resolve this, this paper introduces Expected Bayesian Loss (EBL), a continuous metric that quantifies both the probability and expected severity of metric degradation. Computable directly from standard frequentist estimates, EBL explicitly penalizes empirical noise and high-variance experiments. Validated against expert decisions, EBL provides experimentation platforms with a rigorous, tunable guardrail that aligns statistical safety with institutional risk appetite.

Estimating Uncoded Crash Factors with Tabular Foundation and System One Models: Kumo Tabular and Jev

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10321v1 Announce Type: new Abstract: Road safety programs count the coded fields of police crash records, while the officer's narrative, which often records factors the fields omit, is rarely read. A safety office thus cannot tell how much its counts miss or where to review. This study develops and evaluates a system that joins both views of the 5,601,890 Texas crashes from 2017 to 2025 into population estimates with stated validity. An in-context tabular foundation model, Kumo Tabular, reads the coded record of every crash, a calibrated System One model, Jev, reads the narratives of two probability samples, and human judgments recalibrate its probabilities. A multiwave predict-then-debias estimator joins the three tiers, and a second human tier drawn with recorded probabilities checks the estimates by design. For hydroplaning, medical episodes, fatigue, animals, and phone use, the narrative documents more injury crashes than the coded field, 15,074 against 7,340 for phone use, and the human check agrees with all fifteen estimates within its margin. A re-read list ranked by Kumo Tabular finds confirmed discordance 7 to 58 times as often as random reading. At the planning cost of human coding, one further round of human judgments would cut the root mean square relative half-width from 22.0 to 16.2 percent, against 21.2 for reading every narrative. Two calibrated readers of different views, joined by a sampling design, give a safety office counts, a discordance map, a validated re-read list, and a reading budget, with Kumo Tabular reading the table at 15 times the speed of TabPFN 3.5.

On the Benefit of Blocking for Online Experiments with Skewed Data

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10435v1 Announce Type: new Abstract: This paper advocates for using blocked (stratified) assignment in online A/B tests to handle highly skewed population data. While blocking yields only modest precision gains (5-10%) due to the limits of discretization, the authors demonstrate it offers two crucial structural benefits over post-hoc statistical adjustments. First, fixed-weight blocking correctly targets the true average treatment effect, avoiding the severe bias introduced by efficiency-weighted alternatives. Second, blocking localizes extreme outliers, enabling targeted within-block winsorization that effectively controls noise without destroying the tail-end treatment effect.

Learned Monotone Recurrent Features in Governed Credit Scoring: The Price of the Frame and the Necessity of Macro Conditioning

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.08869v1 Announce Type: cross Abstract: Regulated credit scoring requires scores monotone non-decreasing in every exposure input. Deployed pipelines -- hand-crafted monotone aggregates feeding sign-constrained gradient boosting -- already meet this by composition; the open question is what learned temporal aggregation is worth inside one. We answer on five production-scale credit datasets at matched admissibility (one priced baseline convention excepted), with a monotone recurrent architecture whose per-input guarantee we extend, with proofs, to vector-valued inputs and to exogenously macro-conditioned decay gates, severities, thresholds, and peak memory. Two findings result. First, a strictness ladder: the value of learned monotone features rises with governance-frame strictness -- zero on unconstrained engineered panels, maximal in summaries-only frames -- replicated across two datasets and an official temporal-stability metric, though unconditioned features degrade on externally adjudicated later weeks. Second, a conditioning-delivery asymmetry under regime shift. On a train-on-boom, test-on-crisis mortgage design, two public macroeconomic series hurt as input columns, yet conditioning the recurrence on them delivers the paper's only learned-block crisis-cohort uplifts. The confirmed effect: +0.006 to +0.013 AUC on an internally pre-registered Freddie Mac replication, at all five held-out seeds. The discovery estimate: +0.015 to +0.021 on Fannie Mae (three of five seeds post hoc), worth 10-27 basis points of defaulted balance at an 80% approval cutoff, and grows with early-prepaid loans excluded. A state-level test identifies the mechanism: between-cohort calibration transfer. A pandemic-band episode bounds scope: under forbearance-distorted labels the gain generalizes at a quarter to a third of crisis size on Fannie Mae, on Freddie Mac only against the capacity control.

When Lines Become Contagious: Analyzing the Spread of Infection in the M/M/1 Queue

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09019v1 Announce Type: cross Abstract: In this paper, we construct and analyze a stochastic model for infectious disease spread in service systems. Our model considers a $M/M/1$ queue where a proportion, $p$, of the arriving population is infectious and the remaining population is susceptible. When an infectious person overlaps in the queue with a susceptible customer for more than $\ell$ units of time, then the susceptible person becomes infected. We provide both a personalized perspective of how an individual susceptible customer is infected and a community perspective of how one infectious customer can infect the others around them. From the personalized perspective, we derive the probability that a susceptible person becomes infected and the probability they are infected by at least $k$ different people. From the community perspective we compute the mean and higher moments of the number of susceptible customers that are infected by one infectious individual. Finally, we use stochastic simulation to verify our analytical results and show that our new formulas accurately describe the behavior our stochastic model of infection and to expand our model into the consideration of different arrival and service regimes.

Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09214v1 Announce Type: cross Abstract: Bayesian inference for discrete models with intractable normalizing constants is computationally challenging, particularly when the sample space is large or countably infinite. Although some likelihood-based Bayesian methods can circumvent the intractable normalizing constant, their uncertainty quantification may be poorly calibrated under model misspecification. Generalized Bayesian approaches can address this calibration issue, but typically require careful tuning of a learning rate. In this paper, we propose DFD-BETEL, a semiparametric Bayesian framework that uses the first-order optimality conditions of discrete Fisher divergence as moment conditions in Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of the normalizing constant and requires no learning-rate calibration. We establish consistency and asymptotic normality of the discrete Fisher divergence estimator and prove a Bernstein-von Mises theorem for the DFD-BETEL posterior, showing that its limiting covariance matches the sampling covariance of the estimator and yields asymptotically calibrated uncertainty quantification. Numerical studies show that DFD-BETEL remains competitive with likelihood-based Bayesian inference under correct specification and provides more reliable uncertainty quantification under model misspecification. An application to automobile-insurance claim data further illustrates the practical utility of DFD-BETEL.

Overlapped We Stand, Separated We Fall: Software Approaches to Diagnosing Separation Phenomena in Categorical Response Models

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09951v1 Announce Type: cross Abstract: In statistical models for categorical responses, including binary, nominal and ordinal responses, a phenomenon called ``separation'' may occur which can render maximum likelihood estimate nonexistent and/or nonunique. Based on Sablica et al. (2026)'s general characterization of separation phenomena via structure vectors, in this article we discuss computational, numerical and practical aspects of separation phenomena in different software packages, including consequences, remedies and ways of diagnosing them. We further introduce the R package divoRce which provides the most comprehensive software suite to diagnose separation in existence. It allows to check for separation, to distinguish between types of separation, characterize the recession cone and identify variables and observations contributing to separation for almost any categorical response model in the literature, including models with baseline-category link, cumulative link, adjacent-category link and sequential link specifications. Diagnostics are based on methods for computational geometry and linear programming and can be done in floating-point or rational arithmetic with different solvers. The functionality is easily extendible by wrappers and S3 methods to accommodate implementations in third-party packages or of new categorical response models. We discuss our implementation in detail and show our software in action in a wide range of applications. We recommend to incorporate our checks for separation and existence of the MLE as a diagnostic routine in every categorical data analysis both in third-party software implementations and as part of a standard model diagnostic workflow.

Extreme Binary Classification: Extreme Value Theory for Extreme Constraint on False Negative

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09984v1 Announce Type: cross Abstract: While binary classification is one of the most extensively studied problems in machine learning, the regime in which the goal is to learn a classifier with an almost zero false negative rate remains largely unexplored. In this paper, we introduce the Extreme Binary Classification problem, where the objective is to learn a classifier whose false negative rate $\alpha$ is constrained by $\epsilon_{N_1}=o_{N_1\to\infty}(1/N_1)$, with $N_1$ denoting the number of positive examples in the training set. To address this problem, we propose a threshold adaptation method theoretically grounded in guarantees derived from Extreme Value Theory, together with a feature selection procedure based on a permutation test applied to sample maxima. Experimental results on four real-world datasets of varying sizes demonstrate that our approach compares favorably with state-of-the-art methods. In addition, we illustrate its interpretability through an application to a cancer screening dataset.

Conformal Prediction for Spatially Dependent Data via Sequential Whitening

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10168v1 Announce Type: cross Abstract: Split conformal prediction uses prediction errors on held-out (calibration) data to determine how wide the prediction intervals should be. It guarantees distribution-free finite-sample coverage when these errors and the error at the target site are exchangeable. This assumption may fail under spatial dependence and nonrandom sampling geometry. Existing spatial methods use fitting residuals to remove the predictable part of spatial variation from calibration and target errors. However, the spatial variation that only the calibration residuals can predict remains in both the target and calibration errors, reducing the efficiency and stability of the interval. We address this by additionally conditioning on the calibration residuals sequentially, which scales to large networks through nearest-neighbour approximations. Under a correct working covariance and an elliptical residual law, the resulting interval has exact finite-sample coverage under any spatial design, and under further conditions it is asymptotically oracle efficient. We also bound coverage loss under covariance misspecification and develop a diagnostic that identifies regions at risk of undercoverage. In simulated data, our method produces narrower and more stable intervals than global and localized state-of-the-art alternatives. In a national PM2.5 application, it produces narrower intervals within the network and identifies regions at risk of coverage failure.

Efficient seismic reliability and fragility analysis of lifeline networks using subset simulation

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2310.10232v2 Announce Type: replace Abstract: Various simulation-based and analytical methods have been developed to evaluate the seismic fragilities of individual structures. However, the seismic safety and resilience of a community are substantially affected by network reliability, determined not only by component fragilities but also by network topology and commodity/information flows. Seismic reliability analyses of networks often encounter significant computational challenges due to complex network topologies, interdependencies among ground motions, and low failure probabilities. This paper proposes a variance-reduction method for network fragility analysis using subset simulation to overcome these challenges. The binary network limit-state function is reformulated into more informative piecewise continuous functions. The proposed limit-state functions quantify the proximity of each sample to the network failure domain, thereby enabling the construction of specialized intermediate failure events, which can be utilized in subset simulation and other sequential Monte Carlo approaches. Moreover, by identifying an implicit relationship between intermediate failure events and seismic intensity, we propose a technique to obtain the entire network fragility curve with a single execution of specialized subset simulation. Numerical examples demonstrate that the proposed method can effectively evaluate system-level fragility for large-scale networks.

huff: A Python package for Market Area Analysis

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2602.17640v5 Announce Type: replace Abstract: Market area models, such as the Huff Model and its extensions, are used to estimate regional market shares and customer flows of retail and service locations. In health geography, market area and accessibility models are applied for the analysis of catchment areas and spatial accessibility of healthcare locations. The huff Python package provides a complete workflow for market area and spatial accessibility analysis, including data import, construction of origin-destination interaction matrices, basic model analysis, parameter estimation from empirical data, calculation of distance or travel time matrices, and map visualization. The package is modular and object-oriented. It is intended for researchers in economic geography, regional economics, marketing, geoinformation science, and health geography. The software is openly available via the Python Package Index (PyPI) (https://pypi.org/project/huff/). Its development and version history are managed in a public GitHub Repository (https://github.com/geowieland/huff_official) and archived at Zenodo (https://doi.org/10.5281/zenodo.18639559). A methodological handbook is also available on GitHub Pages (https://geowieland.github.io/huff_official/).

Evaluating LiDAR Data Sources, Predictor Resolution, and Spatial Random Effects in Bayesian Change-of-Support Models for Forest Inventory

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.06476v2 Announce Type: replace Abstract: Forest managers need timely stand-level information to support operational planning, particularly in mixed-species, structurally heterogeneous forests facing climate-related disturbance. Model-based estimation combines sparse field data with remotely sensed predictors to estimate growing stock volume (GSV) for small areas. While uncrewed aerial vehicle laser scanning (ULS) offers flexible, high-resolution LiDAR acquisition, its advantages over conventional airborne laser scanning (ALS) remain unclear. We compared publicly available ALS and newly acquired ULS data using Bayesian change-of-support models to estimate GSV in a mixed-species forest in north-eastern Germany. We evaluated distributional LiDAR metrics and spatial random effects. ULS consistently outperformed ALS, achieving cross-validated RMSPEs of 68.5 m^3/ha and 79.5 m3/ha, respectively-a 13.8 % reduction in prediction error. Distributional metrics improved ULS models more strongly, reducing RMSPE by up to 10.1 %; spatial effects provided only minor gains at substantially higher computational cost. ULS also produced lower uncertainty in latent stand-mean GSV estimates. The ULS advantage may reflect both finer-scale canopy information and closer temporal alignment with field measurements. Timely, information rich LiDAR may therefore be more valuable for stand-level GSV estimation than increasingly complex spatial models. Temporally matched ALS-ULS comparisons are needed to isolate platform effects.

DeepAJM: Deep Association Joint Model for Irregularly Sampled data

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.07388v2 Announce Type: replace Abstract: Joint Models simultaneously model longitudinal and survival outcomes, leveraging patterns in patients' longitudinal trajectory to improve the prediction of survival outcomes. The classical parametric joint models, however, rely on fixed parametric assumptions, making them susceptible to bias under model misspecification and smaller sample sizes. We propose a deep joint model, DeepAJM, that does not require any parametric assumptions, while retaining a partially interpretable, per-longitudinal-outcome association structure. The joint model uses an encoder-decoder (sequence-to-sequence) architecture to learn the latent structure in patients' time-varying covariate trajectories. The model links the longitudinal processes to the survival processes through a learned interpretable association structure, in which each longitudinal output from the decoder gets remodulated by baseline covariates before it contributes to the risk scores from the survival head of the architecture. The model was evaluated on three datasets ( a cardiovascular-disease EHR cohort, a primary biliary cirrhosis (PBC2) dataset, and a simulated dataset) against a classical parametric joint model, TransformerJM, DA-LSTM and a Cox-based survival-only model. All models were assessed using C-index, integrated brier score (IBS), time-dependent AUROC, and time-dependent AUPRC. Our model achieved the best discrimination in terms of the C-index, time-dependent AUROC, and AUPRC across all datasets.

Robust Bayesian methods using amortized simulation-based inference

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2504.09475v2 Announce Type: replace-cross Abstract: Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been much recent work on modified SBI approaches which are robust to misspecified likelihoods. However, less attention has been given to the issue of inappropriate prior specification, which is the focus of this work. In conventional Bayesian modelling, there will often be a wide range of prior distributions consistent with limited prior knowledge expressed by an expert. Choosing a single prior can lead to an inappropriate choice, possibly conflicting with the likelihood information. Robust Bayesian methods, where a class of priors is considered instead of a single prior, can address this issue. For each density in the prior class, a posterior can be computed, and the range of the resulting inferences is informative about posterior sensitivity to the prior imprecision. We consider density ratio classes for the prior and implement robust Bayesian SBI using amortized neural methods developed recently in the literature. We also discuss methods for checking for conflict between a density ratio class of priors and the likelihood, and sequential updating methods for examining conflict between different groups of summary statistics. The methods are illustrated for several simulated and real examples.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2509.08483v2 Announce Type: replace-cross Abstract: We analyze gradient descent with Polyak (1964) heavy-ball momentum (HB) whose fixed momentum hyperparameter $\beta \in (0, 1)$ provides exponential decay of memory. Building on Kovachki and Stuart (2021), we prove that on an exponentially attractive invariant manifold the algorithm is exactly plain gradient descent with a modified loss, provided that the step size $h$ is small enough. Although the modified loss does not admit a closed-form expression, we describe it up to $O(h^{\mathcal{R}})$-errors for arbitrary finite order $\mathcal{R}$, and prove global (finite "time" horizon) trajectory approximation bounds $O(h^{\mathcal{R}})$. We then conduct a fine-grained analysis of the combinatorics underlying the memoryless approximations of HB, in particular, finding a rich family of polynomials in $\beta$ hidden inside which include and lie coefficient-wise in between Eulerian and Narayana polynomials. We prove that these polynomials are $h$-polynomials of certain graph-associahedra. As corollaries of the main results, we derive continuous modified equations of arbitrary finite approximation order (with rigorous bounds) and the principal flow that approximates the HB dynamics, generalizing Rosca et al. (2023). Approximation theorems cover both full-batch and mini-batch HB. The results shed new light on the main features of HB and outline a roadmap for similar analysis of other optimization algorithms.

Continuous mixtures of Gaussian processes as models for spatial extremes

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2602.09512v2 Announce Type: replace-cross Abstract: Spatial modelling of extreme values allows studying the risk of joint occurrence of extreme events at different locations and is of significant interest in climatic and other environmental sciences. A popular class of dependence models for spatial extremes is that of random location-scale mixtures, in which a spatial "baseline" process is multiplied or shifted by a random variable, potentially altering its extremal dependence behaviour. Gaussian location-scale mixtures retain benefits of their Gaussian baseline processes while overcoming some of their limitations, such as symmetry, light tails and weak tail dependence. We review properties of Gaussian location-scale mixtures and develop novel constructions with interesting features, together with a general algorithm for conditional simulation from these models. We leverage their flexibility to propose extended extreme-value models, that allow for appropriately modelling not only the tails but also the bulk of the data. This is important in many applications and avoids the need to explicitly select the events considered as extreme. We propose new solutions for likelihood inference in parametric models of Gaussian location-scale mixtures, in order to avoid the numerical bottleneck given by the latent location and scale variables that can lead to high computational cost of standard likelihood evaluations. The effectiveness of the models and of the inference methods is confirmed with simulated data examples, and we present an application to wildfire-related weather variables in Portugal. Although not detailed here, the approaches would also be straightforward to use for modelling multivariate (non spatial) data.

The generalized lower triangular process prior

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09762v1 Announce Type: cross Abstract: In the analysis of multivariate data, factor models represent a powerful technique for both reducing dimensionality and facilitating qualitative understanding of the latent determinants governing the observed data. Interpretability, however, is often hindered by the non-identifiability of factor loading matrices due to rotational invariance. A prevailing strategy to address this issue is to consider positive lower triangular structures. A relaxation of the latter condition has been recently proposed in the literature with the so called generalized lower triangular structure. However, its Bayesian implementation presents substantial challenges, requiring complex reversible-jump algorithms and making prior elicitation difficult because of the limited interpretability of the model parameters. In this paper, we introduce a generalized lower triangular process prior that allows both global and within-component sparsity structures for learning both the number of factors and possible sparsity structures within the vector of observations. The proposed approach provides straightforward prior parameters elicitation exploiting possibly different prior information on the rank and sparsity characteristics. We also explore connections with the Indian buffet process, providing further insight into the sparsity structure induced by the proposed prior. Posterior computation can be performed resorting to a Gibbs sampler with Metropolis-Hastings moves. The efficacy of the proposed method is demonstrated through comprehensive simulations and the analysis of the Big Five Personality Test data.

Graph-monotone entrywise guarantees for MLE and Rank Centrality on general comparison graphs

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09030v1 Announce Type: new Abstract: Pairwise comparisons are widely used to infer latent scores and identify top-ranked items. Although sharp statistical guarantees are available under uniform sampling, real data often induce irregular comparison graphs with heterogeneous observation counts across pairs. In this paper, we study an arbitrary fixed comparison graph under the Bradley--Terry--Luce model with minimal assumptions. We prove that both the standard maximum likelihood estimator and Rank Centrality achieve a high-probability entrywise error rate of order $1/\sqrt{\lambda_{\mathcal{D}}}$ up to logarithmic and dynamic-range factors, where $\lambda_{\mathcal{D}}$ is the algebraic connectivity of the count-weighted observation graph. This guarantee is graph-monotone since $\lambda_{\mathcal{D}}$ cannot decrease when additional comparisons are added. Under heterogeneous sampling, where comparison pairs are sampled independently with unequal probabilities, our guarantee improves existing error bounds or requires weaker assumptions. We further extend our analysis to show that both estimators are robust against outcome-adaptive augmentation, where an adversary can choose additional comparison pairs after observing the initial outcomes.

Local asymptotic normality for spectral-tail likelihoods under fixed-domain sampling

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09105v1 Announce Type: new Abstract: We establish local asymptotic normality (LAN) for joint inference on scale and roughness in stationary Gaussian random fields observed on increasingly dense regular grids in a fixed domain. Scale and roughness are represented by the coefficient and decay exponent of the leading spectral tail. Under spectral regularity conditions, we identify the joint normalization governing the LAN expansion and prove consistency and asymptotic normality of the maximum likelihood estimators. For $N$ observations, the estimation errors are of order $N^{-1/2}$ for roughness and $(\log N)/\sqrt N$ for scale. After componentwise normalization, the errors converge to a perfectly correlated Gaussian pair. Knowing either parameter improves the convergence rate for estimating the other by a logarithmic factor. The analysis uses generalized locally Toeplitz (GLT) theory, for which we develop a truncation principle accommodating nonintegrable limiting symbols and quantitative bounds on the contribution from low frequencies. We verify the assumptions for Mat\'ern and generalized Wendland covariance families, establishing uniform spectral bounds for the latter. We also show that consistency and the limiting distributions persist under covariance misspecification when the true and fitted spectra share the same leading tail and their difference decays sufficiently rapidly. This includes misspecification between Mat\'ern and generalized Wendland models under explicit parameter restrictions.

Sharp and Adaptive Cluster Recovery in Slowly Mixing Gaussian Hidden Markov Models

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09123v1 Announce Type: new Abstract: We study cluster recovery in a two-state Gaussian hidden Markov model in the slowly mixing regime, where the transition probability $\delta$ may vanish with the sample size. Temporal persistence creates long homogeneous segments and fundamentally changes the recovery problem relative to the i.i.d. Gaussian mixture benchmark. Rather than being purely adverse, label dependence provides exploitable structure: the statistical difficulty becomes concentrated near the rare transition points, giving rise to recovery regimes governed explicitly by their frequency $\delta$. We first characterize, up to universal constants, the oracle Bayes risk for offline and online clustering. Both problems exhibit a nonstandard polynomial risk regime, but the sequential constraint induces an additional logarithmic localization cost, yielding a genuine online/offline gap. We also study fixed lag prediction with delayed label feedback and identify the effective memory horizon beyond which past labels no longer improve the optimal rate. When the signal direction is unknown and possibly high dimensional, the problem is governed by the effective signal strength \[ r_n^2 = \frac{\|\theta\|^4/\sigma^4} {\|\theta\|^2/\sigma^2+d/n}. \] We derive minimax lower bounds and construct fully adaptive polynomial time procedures attaining the sharp recovery rates. In particular, almost full recovery is possible precisely when $r_n^2\gg\delta$. If $n\delta\gtrsim\log n$, adaptation to both the signal $\theta$ and the transition probability $\delta$ incurs no first order loss, and the sharp exact recovery threshold (under the Hamming loss) is \[ r_n^2 = 2\log(n\delta)\,(1+o(1)). \] Thus the effective complexity of the problem is governed by the number of latent transitions, rather than by the sample size itself.

Low-Order Inclusion Probabilities Do Not Determine Asymptotic Normality

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09168v1 Announce Type: new Abstract: Central limit theorems in survey sampling are typically established under specific sampling designs rather than from generic characteristics of a design. Motivated by the search for more general conditions, we investigate whether low-order inclusion probabilities can provide such a basis. First- and second-order inclusion probabilities determine the first two moments of sampling estimators such as the Horvitz--Thompson estimator, but we show that even exact agreement of these probabilities with those of simple random sampling without replacement (SRSWOR) does not preserve asymptotic normality. We construct a sequence of fixed-size sampling designs having exactly the same first- and second-order inclusion probabilities as SRSWOR, together with a sequence of finite populations for which the sample total converges to $N(0,1)$ under SRSWOR but to a centered standard exponential distribution under the alternative designs. Thus, the two sample totals have exactly the same mean and variance at every stage of the sequence, yet have different limiting distributions. The alternative designs are obtained from balanced incomplete block designs arising from finite projective planes. Their cyclic structure allows us to prescribe the distribution of the sample total under block sampling, while a probabilistic permutation argument, combined with an exponential inequality for sampling without replacement, yields finite populations satisfying the SRSWOR central limit theorem. The result shows that low-order inclusion probabilities do not control the global dependence structure relevant to asymptotic normality and therefore cannot, by themselves, provide general conditions for central limit theorems under complex sampling designs.

Tightness and Error Exponents of SDP with Logarithmically Many Communities

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09303v1 Announce Type: new Abstract: We study a semidefinite programming (SDP) relaxation for community recovery when the number of communities grows logarithmically. In the balanced stochastic block model with $n=km$ vertices, we consider the regime $k/\log m\to\gamma>0$, with edge probabilities $\alpha\log m/m$ within communities and $\beta\log m/m$ across them, for fixed $\alpha>\beta>0$. We derive the sharp asymptotic tightness boundary away from critical cases. When rare vertices cause tightness to fail while the bulk remains spectrally stable, the normalized matrix error of every near-optimal solution still vanishes. We prove matching high-probability exponents for this error and the normalized optimal objective gain, governed by the same local correction that determines tightness. Throughout this spectrally stable region, a single SDP solve followed by explicit rounding and refinement achieves exact community recovery above the information-theoretic threshold. This guarantee holds even when the planted community matrix is not an optimal solution to the SDP.

The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09687v1 Announce Type: new Abstract: Structured recovery phenomena, such as restricted isometry properties in compressed sensing, have shown that high-dimensional objects can often be reconstructed from remarkably low-dimensional linear measurements. This work develops an analogous recovery framework for low-rank signed measures on $\mathbb{R}^2$, defined here as measures that can be expressed as finite sums of product measures with one-dimensional factors. The framework is based on linear operators, termed "silhouette operators," that map a measure to a fixed finite collection of one-dimensional linear pushforwards. The main results show that a suitably chosen collection of $2k$ projected marginals suffices to identify every compactly supported rank-$\le k$ signed measure, that this number is optimal, and that the projection directions cannot be chosen arbitrarily. The framework is also extended to higher-dimensional sums of product measures by establishing sufficient conditions under which collections of pairwise marginals identify the full model. Building on this framework, a computationally efficient estimator, termed "silhouette mixture estimation" (SME), is introduced for constructing a low-rank empirical measure from data by matching its one-dimensional projected marginals to the corresponding empirical marginals in Wasserstein distance. When combined with one-dimensional density estimators, SME yields an efficient nonparametric density estimator that performs strongly relative to a range of parametric, nonparametric, and deep-learning baselines in settings of moderate dimension and sample size.

Unbounded Characteristic and Universal Kernels

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09731v1 Announce Type: new Abstract: Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense success stems from the flexible function class associated to each kernel---its reproducing kernel Hilbert space (RKHS)---which facilitates statistical analysis, as well as from their computational tractability and applicability to many domains. Multiple notions (such as characteristic, $L_p$-universal, and integrally strictly positive definite) capture the expressivity of kernels and their RKHSs and play a key role in understanding the statistical properties of kernel methods; these concepts and their relations are well-understood for bounded kernels. Even though unbounded kernels have received significant attention over the past decade (for instance, in the construction of kernel-based discrepancy and dependence measures such as the maximum mean discrepancy, the Hilbert-Schmidt independence criterion, and the kernel Stein discrepancy), surprisingly little is known about the relations of these notions in the unbounded case. In the present paper we tackle this severe bottleneck, establishing their relations under mild assumptions.

Drift Estimation for a Multi-Dimensional L\'evy-Driven Stochastic Differential Equation Using Deep Neural Networks

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09813v1 Announce Type: new Abstract: We develop a non-asymptotic theory for nonparametric drift estimation in discretely observed multi-dimensional L\'evy-driven stochastic differential equations using sparse ReLU neural networks. Under exponential $\beta$-mixing and an exponential-tail condition on the L\'evy measure, we establish an oracle inequality for the least-squares estimator. The jump component changes both the martingale structure and the concentration regime relative to diffusion models: continuous martingales are replaced by discontinuous martingales, while the relevant empirical-process fluctuations are sub-exponential rather than sub-Gaussian. We handle these difficulties without truncating the observed increments, using an exponential-supermartingale argument for compensated Poisson integrals and $\psi_1$-chaining. Despite the weaker concentration, the resulting statistical bound is, up to constants, of the same order as the corresponding diffusion bound. For drift functions with hierarchical compositional structure, this yields intrinsic-dimensional convergence rates. The framework allows infinite jump activity and, in some cases, infinite variation. Finally, we establish a minimax lower bound on a fixed non-trivial compound-Poisson submodel. Together with the upper bound, this shows that the estimator is minimax optimal up to logarithmic factors.

Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10080v1 Announce Type: new Abstract: Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the kernel parameters are routinely estimated by the maximum likelihood estimators (MLEs), as implemented by standard GP software. Despite this widespread use, the asymptotic behavior of the MLEs remains poorly understood under fixed-domain asymptotics, even for the RBF kernel. The main difficulty arises from the increasingly strong dependence among densely sampled observations and the nonlinear dependence of the covariance matrix on the kernel parameters. In this paper, we address this gap by providing, to the best of our knowledge, the first complete asymptotic characterization of the joint MLE of the spatial variance, lengthscale, and nugget variance under fixed-domain asymptotics. We establish consistency, derive convergence rates for all three parameters, prove joint asymptotic normality, and show that these rates are minimax optimal.

A polyhedral framework for hierarchical Archimedean copulas: estimation, hierarchy recovery and singular asymptotics

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.10134v1 Announce Type: new Abstract: Hierarchical Archimedean copulas (HACs) admit redundant tree representations: when adjacent internal nodes have equal parameters, contracting the connecting edge leaves the copula unchanged. This creates a structural overparametrization. For homogeneous one-parameter families, we remove this redundancy and identify the resulting reduced model class with the ultrametric fan. We treat the Clayton, Frank, Ali-Mikhail-Haq, Gumbel and Joe families. Using the negative logit of normalized Kendall's tau as a common node-height coordinate, reduced hierarchies form polyhedral strata, binary hierarchies index maximal cones, and multifurcating hierarchies lie on common contraction faces. The induced cophenetic metric generates the same topology as uniform convergence of copulas. We also show that informative pairwise dependence summaries act componentwise on cophenetic coordinates and hence provide global coordinates for the reduced model. This representation yields a global estimator obtained by inverting estimated pairwise summaries and projecting onto the fan, without preselecting a hierarchy. We prove consistency and convergence-rate transfer. At binary truths, the unthresholded estimator recovers the hierarchy with probability tending to one; at multifurcating truths, it asymptotically selects a binary refinement, while vanishing thresholding consistently recovers the reduced hierarchy. Under a joint central limit theorem for the pairwise summaries, the projected estimator has a root-$n$ limit given by Euclidean projection of a Gaussian vector onto the tangent fan. The limit is Gaussian at binary hierarchies and generally non-Gaussian at multifurcating ones. For empirical Kendall's tau, we verify the required regularity conditions and obtain the corresponding singular limit.

Slow Beats Fast at the Kesten-Stigum Threshold: Minimax, Fisher-Information and Belief-Propagation Characterizations of the Information-Computation Gap in Sparse Stochastic Block Models

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.08872v1 Announce Type: cross Abstract: We study community recovery in the sparse symmetric stochastic block model with $q$ communities, average degree $d$ and signal strength $\lambda$ through statistical decision theory and Fisher information, and obtain three characterizations of the Kesten-Stigum threshold $d\lambda^2=1$ and of the information-computation gap below it. First, on each community-size profile the minimax risk of any class of rules closed under averaging and vertex relabeling equals its Bayes risk under the uniform prior; the posterior mean is the unique Bayes rule and is admissible, and the Bayes risk of degree-$D$ polynomial rules is the trivial risk times $1-\mathrm{Corr}_D^2$. Combined with known low-degree and information-theoretic results, this gives the gap as a worst-case statement: for $q\ge 5$ there is a window below the threshold in which no low-degree rule beats the trivial risk asymptotically, while an exponential-time rule does on a set of labelings of probability $1-o(1)$. Second, the Fisher information about $\lambda$ carried by cycle counts is a series with terms of order $k(d\lambda^2)^k$, convergent exactly when $d\lambda^2 1$ of Chin et al. for $q=n^\chi$ communities and identifies personalized PageRank as a walk count with suboptimal weights. Experiments on networks with up to $3\times 10^5$ vertices confirm the threshold for $q=2$, the hard window for $q=5$, and the many-community scaling.

Projected Normal Models on Recursively Curved Tori

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.08974v1 Announce Type: cross Abstract: We develop a computationally tractable statistical framework for angular data supported on a recursively embedded curved torus $\mathbb{T}^n\hookrightarrow\mathbb{R}^{n+1}$. Due to the recursive structure we build an exact uniform sampler by generalizing the process from the curved 2-torus. We generalize projected normal distributions to the curved $n$-torus and we develop inference theory for these distributions. We utilize both maximum-log-likelihood estimates and energy-based Fr\'echet estimates for the projected normal distribution for this purpose. This is done by establishing identifiability for isotropic projected normal distributions and by applying theory of maximum likelihood and intrinsic statistics for the curved tori. We numerically verify the geometry, sampler, density transformation, and energy solver. Lastly, we demonstrate the applicability of the proposed model using real data.

On the Computational Complexity of Hidden Markov Model Identification

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09104v1 Announce Type: cross Abstract: Identification is the task of recovering the parameters of an unknown ground-truth model from sampled data. When parameters other than the ground truth induce the same output distribution, data alone does not provide enough information to recover the ground truth, and the model is thus called unidentifiable. We study the identifiability problem for hidden Markov models (HMMs): given an HMM, is it identifiable? Existing work on HMM identification establishes conditions under which the ground-truth HMM can be identified. However, most of these conditions are sufficient but not necessary, meaning that, when a model does not satisfy them, its identifiability remains inconclusive. We instead take a computational perspective: is there a sound and complete algorithm that decides whether a given HMM is identifiable, and if so, what is the complexity of this decision problem? We consider the decision problems arising from the various notions of identifiability in the literature, including deterministic, generic, global, local, state-permutation- invariant, and finite-alphabet identifiability. We show that all of these problems are decidable in PSPACE, via reductions to the theory of the reals at various levels of its quantifier-alternation hierarchy. We further show that the deterministic variants are already coETR-hard (and hence coNP-hard) for simply parameterized families.

Sketched Calibration for Conformal Prediction under Covariate Shift

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09208v1 Announce Type: cross Abstract: Weighted conformal prediction corrects for covariate shift by reweighting calibration scores with the likelihood ratio between target and source covariates. Its cost grows with the chi-square divergence between the two covariate laws, typically exponentially in the size of the shift, and much of it can be paid for shift in directions that do not affect the response. We propose sketched calibration: weighted conformal prediction with the ratio of compressed covariates $Z=T(X)$, used in the weights and optionally in the score. Compression never increases the shift-dependent calibration cost, and target coverage is at least $1-\alpha-\Delta_T$, where the leakage $\Delta_T$ measures how much of the discarded shift reappears as a change in the law of the response, or of the score, given $Z$. The leakage is a covariance between the discarded shift and the response on the fibres of the sketch; it vanishes when the sketch is sufficient or retains the shift, and a minimax construction shows that no threshold rule for a fixed score can avoid it. In a heteroscedastic simulation where unweighted calibration fails, a one-dimensional sketch cuts the fraction of infinite prediction sets from $37.8\%$ to $8.0\%$ at mean coverage $92.3\%$ for a $90\%$ target; nonlinear and real-data experiments show when learned sketches succeed and when they fail.

Witnessing Quantum Bayesian Inference beyond Classical Learning

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09293v1 Announce Type: cross Abstract: Can an agent's predictions reveal whether its reasoning is based on a classical or a quantum model? Using known results on matrix factorizations, here we show that quantum Bayesian retrodiction can produce one-step-ahead forecasts incompatible with every classical Bayesian explanation based on learning about a fixed but unknown sampling law from conditionally independent observations. The separation has a sharp threshold in the number of outcomes: for any measurement with at most four outcomes, the quantum predictions admit a classical realization, irrespective of the prior state and the finite Hilbert-space dimension, whereas a five-outcome measurement on a single qubit already violates an explicit classical bound. This bound holds for arbitrary classical latent states, prior probabilities, and sampling laws, and involves only the agent's initial and updated predictions. Thus, in this setting, quantum Bayesian retrodiction is strictly more expressive than classical Bayesian learning, and this difference can be witnessed without observing or specifying the agent's internal description.

The Geometry of Anisotropic Dilation for Optimal Regularization

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09310v1 Announce Type: cross Abstract: A central question in data-driven inverse problems is how to construct a regularizer that adapts to the geometry of the data distribution. Recent work in optimal regularization shows that, within a broad Gibbs class, the regularizer best matched to a distribution $P$ is determined by a single, direction-dependent radial summary statistic $\rho_P$. This suggests a way to control regularizer geometry by transforming the data. In particular, which transformations act on $\rho_P$ in a simple, explicit way? Can they improve the optimization properties of the resulting variational problems or adapt a fixed base regularizer to data? To address these questions, we introduce anisotropic dilation, a direction-preserving map that rescales each point along its Euclidean ray by a positive profile on the sphere. Despite its simplicity, this family acts transitively on the space of radial summary statistics: any target regularizer in the Gibbs class can be reached from any source distribution by a single explicit profile. We characterize the resulting orbit structure on distributions, derive in closed form the profile that optimally adapts a fixed base regularizer to the data, and show that its improvement over isotropic rescaling is governed by a Jensen gap that is provably positive for several natural families. We also establish finite-sample generalization bounds for jointly learning the base regularizer and anisotropic profile, with explicit rates when the logarithm of the profile is parameterized by linear feature models or sparse ReLU networks. Building on this theory, we parameterize the base regularizer and anisotropic profile and learn them jointly from samples, yielding a data-adaptive regularizer for variational inverse problems. Experiments on a controlled two-dimensional family and MNIST denoising show that learning the profile further improves performance.

Sequential resetting procedures and false discovery rate

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09339v1 Announce Type: cross Abstract: Data arrive sequentially, each associated with a null hypothesis. We develop testing procedures to locate intervals in which some null hypotheses fail with false discovery rate (FDR) control. The new procedures are called sequential resetting procedures, and they are based on e-values and test supermartingales. We also develop a refined version of the procedures by dropping less informative data points before the block minimum of the test supermartingale in each rejection block. These procedures have explicit FDR bounds under two settings: a classic setting of independence and the more general setting of possible dependence across null data and non-null data. These FDR bounds are independent of the testing horizon, and the general one has anytime validity, but it has an extra logarithm factor compared with the standard FDR level. We present simulation studies and data experiments with applications of sequential resetting procedures to LLM watermark detection and financial backtesting.

Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09452v1 Announce Type: cross Abstract: Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location. Logistic Gaussian processes (LGP) give a flexible prior for such densities. However, the normalizing constant of an LGP has no closed form, so existing methods approximate or replace the likelihood. We propose the exact likelihood finite-rank LGP (ExFR-LGP), which writes the log density as the sum of two bivariate functions, one of the response and a location-varying linear index of the covariates, and one of the response and the location. Each function is assigned a finite-rank Gaussian process prior that is piecewise linear on a regular grid, enabling the normalizing constant, the conditional mean and the quantiles to enjoy closed form representations. Posterior samples are drawn from the exact posterior under this prior via a Gibbs sampler that updates the Gaussian components by elliptical slice sampling. When the true log density is the sum of two such bivariate functions, we show that the posterior contracts at the minimax rate of an $\alpha$-smooth bivariate density up to a logarithmic factor. Numerical experiments using synthetic data demonstrate the effectiveness of ExFR-LGP in conditional density estimation. Furthermore, application to fractional anisotropy responses along the corpus callosum in the Alzheimer's Disease Neuroimaging Initiative data yields covariate-adjusted percentile bands with uncertainty, elucidating how diagnosis changes the distribution along the tract.

Fluctuations of Nonlinear Observables in Mean Field Neural Network Training

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09768v1 Announce Type: cross Abstract: Mean field limits describe the training dynamics of wide neural networks through the evolution of the empirical distribution of their parameters. Although functional central limit theorems characterize the asymptotic fluctuations of this distribution, quantities of practical interest are typically nonlinear observables of the parameter distribution rather than the distribution itself. In this work, we show how these mean field fluctuations propagate to finite dimensional nonlinear observables for shallow neural networks trained by stochastic gradient descent. Working in the weighted Sobolev space in which the limiting fluctuation process is constructed, we apply a functional Delta method under ordinary Fr{\'e}chet differentiability, without requiring Lions derivatives with respect to the measure variable. We obtain a central limit theorem for the observables and, under a suitable representation of their differentials, an explicit covariance formula inherited from the underlying mean field fluctuation theory. We also study whether prescribed quantities of interest can be recovered from the selected observations. Under a constant rank assumption, we prove that a quantity of interest factors locally through the observation functional if and only if, throughout a neighborhood, the kernel of the differential of the observation is contained in that of the quantity of interest. Thus, a differential condition expressed directly in the ambient Sobolev space yields an exact nonlinear local factorization. These results provide a framework both for quantifying finite-width uncertainty on observable, statistically or physically meaningful quantities and for assessing whether the chosen observations contain the information required to identify them.

Outperformance Inverse Optimization: Learning Objective Functions that Outperform Agent Decisions

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09890v1 Announce Type: cross Abstract: Inverse optimization estimates the weights of an objective function that explain observed decisions as optimal solutions, and is used in a variety of fields. For mixed-integer linear programs (MILPs), existing methods aim to reproduce the observations as optimal solutions, and thus learn compromise weights when the observations are suboptimal. We propose outperformance inverse optimization, which instead seeks weights that induce, at each state, an optimal solution outperforming the observed action in every component. We give a loss function that can be evaluated with forward-problem oracles alone and is thus applicable to MILPs, together with gradient-based and DC optimization algorithms for minimizing it. For weights inducing a unique outperforming optimal solution at all observations, we prove that the probability of failing to induce such a solution at a new state (the generalization error) is bounded by a quantity inversely proportional to the number of observations, and that this bound is tight in the number of observations up to logarithmic factors. In experiments on synthetic and real data, the proposed methods improve the prediction of solutions outperforming the actions over existing methods.

Weighted NPMLE for the Marginal Mean of Recurrent Events with a Competing Terminal Event

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2605.25934v4 Announce Type: replace-cross Abstract: Regression modeling of recurrent and terminal events continues to present methodological challenges in survival analysis. Existing approaches either make unverifiable assumptions about the dependency structure between the two event types or rely on the proportional intensity assumption for the marginal mean. A semiparametric regression model is proposed that is based on a novel weighted likelihood function, thereby targeting directly the marginal mean of the recurrent event. Our general model captures a large class of semiparametric regression models and accommodates external time-dependent covariate effects on the marginal mean intensity. We establish the consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. We propose a novel simulation procedure that directly targets the marginal mean intensity of the recurrent events. In simulation studies, we demonstrate a strong performance of the weighted NPMLE under independent right-censoring. The practical utility of the proposed methodology is demonstrated through application to data from the STATCOPE trial, a large randomized clinical trial that investigated the efficacy of simvastatin for COPD exacerbations. We provide personalized predictions for the number of exacerbations and reassess the effect of simvastatin treatment, accounting for death as a competing terminal event for patients with GOLD stage 4.

A Formal Graphical Inference Framework for Combining Effect Size with Statistical Significance: Application to Multivariate and Functional Linear Models

Thu, 08 Oct 2026 00:00:00 -0400

arXiv:2610.09094v1 Announce Type: cross Abstract: To address the critical need for statistical methods that evaluate practical magnitude alongside statistical significance, we introduce a formal graphical inference framework that intrinsically combines effect size with uncertainty. Built upon resampling and global envelopes, this approach provides universality and direct visual interpretability. While existing envelope tests provide only weak family-wise error rate (FWER) or false discovery rate control, we advance the methodology by introducing novel step-down global envelopes. We theoretically prove that several of these envelopes achieve exact strong FWER control under exchangeability, guaranteeing rigorous inference for each individual local hypothesis. Beyond yielding adjusted $p$-values, the framework provides adjusted subset $p$-values for blocks of hypotheses, such as the functional effect of a covariate within a specific category. By explicitly visualizing the size and direction of the effect relative to its variability under the null hypothesis, our approach overcomes the dichotomous nature of traditional testing and provides profound informational value. The proposed framework is applied to multivariate and functional linear models.

Beyond Marginal Monitoring: Distributed Joint-Distribution Testing for Data Concept Drift in Large Scale E-Commerce Operations

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08132v1 Announce Type: cross Abstract: Concept drift threatens production machine learning, yet the empirical behavior of multivariate two-sample drift detectors at scale remains under-characterized. Existing benchmarks rarely address the hundreds of millions of rows and high-cardinality features typical of industrial-operational datasets. We evaluate five multi-column two-sample tests (marginal, projection-based, and kernel embedding methods) across three complementary environments: the Harvard Dataverse, a validated Failing Loudly reproduction (mean absolute error between 0.030 and 0.053), and a novel synthetic-injection benchmark on the 137.5-million-row Trendyol collection-ranking feature table. Testing four drift types across two severity-scope regimes, we demonstrate that distributed Maximum Mean Discrepancy with Random Fourier Features on Apache Spark scales robustly. Averaged over the four drift types in the strong regime and under a calibrated threshold, it achieves a Pearson correlation of r = 0.940 with expected drift magnitude, an 80.4% true positive rate, and a 3.2% false positive rate. Conversely, the per-dimension Kolmogorov-Smirnov test failed due to statistic saturation from ID-like columns under asymmetric sampling, establishing a critical constraint for large-scale sampling design. At weak configurations (realized-flip fractions of at most 0.57%), detectors struggled to reliably discriminate, highlighting the need for future intensity-grid power analyses to distinguish fundamental sensitivity bounds from scalable threshold shifts.

A Functional Representation of Credit Behavior for Probability of Default Modeling

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07888v1 Announce Type: cross Abstract: This paper proposes a framework for modeling probability of default via functional data analysis. By representing a series of credit variables as functions, we investigate whether intra-monthly information improves default predictability in linear models. We further show how a range of widely used variables, among them available funds, utilization rate, and overdraft, can all be derived from three quantities observed over time. Namely, 1) the type of each account, 2) the balance of the account, and 3) the size of the credit limit on the account. Retaining these quantities as continuous-time processes, rather than reducing them to monthly aggregated values, yields a continuous faithful representation of the borrower. When analyzing these three processes, we discovered that recurring events associated with the ordinal position among banking days created strong cyclical patterns. We therefore develop a relative time framework that aligns the recurring events across borrowers, ensuring that borrowers possess the same cyclical pattern, regardless of real time. We assess the framework using functional logistic regression. This approach accommodates the continuous representation while remaining closely related to a logistic regression model commonly used in credit risk practice, due to strict regulatory constraints. We show that, when equipped with an effective functional representation of transactional trajectories, the proposed model attains predictive performance on par with XGBoost while consistently outperforming logistic regression. Importantly, the model balances predictive performance of a machine learning model with the interpretability of linear default models, potentially enabling financial institutions to use the model, even under strict regulation.

Prediction-powered inference for time series across space

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08715v1 Announce Type: new Abstract: The following motif is common in spatiotemporal settings: we have a sequence of covariate and label pairs observed for a relatively short, recent time period. We have access to unlabeled covariates over a longer time period. Data is observed over many spatial locations. For instance, crop yield might be observed over a large geographical area for recent years, but weather data (which is informative about crop yield) is available for a much longer period. The goal is to estimate, at each spatial location, the expected label (e.g., crop yield) in the future and provide a valid confidence interval for this value. The observed time period alone is too short for reliable estimates. Imputing missing labels with machine learning can cause substantial bias. Prediction-powered inference (PPI) can correct for this bias, but it relies on an i.i.d. assumption that breaks under our expected temporal dependencies. Heteroskedasticity and autocorrelation consistent (HAC) procedures account for temporal correlation, but have not been adapted to cases where some labels are imputed. We provide reliable point estimates and confidence intervals given: short labeled time series (across spatial locations), a longer unlabeled time series, and an imperfect predictor of labels given covariates. We show our method outperforms natural alternatives.

When does conformal calibration need censoring weights? Cause-of-failure prediction sets under competing risks

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08602v1 Announce Type: new Abstract: Split conformal prediction sets for competing-risks labels at a fixed horizon require calibration labels that right censoring can leave unobserved. Complete-case calibration guarantees coverage for the label-complete subpopulation, but its population coverage can deviate in either direction, even at the true class probabilities. We study how selection changes the score distribution near the population quantile. At the true score in our main simulation family, with independent draws, complete-case calibration covers 0.8723 at a nominal 0.900 when 22% of subjects are event-free at the horizon. In 4 of 48 further designs using per-draw normalisation, estimating cause incidences as one minus the exponential of the negative of the cause-specific Nelson-Aalen cumulative hazards, with the event-free probability as the clipped and renormalised remainder, puts complete-case coverage at least four standard errors below nominal. In these designs, weights from a correctly specified censoring model keep coverage near nominal. Extending the argument of Yi et al. (2025) to a cause label, we establish a finite-sample coverage lower bound with an explicit penalty for censoring-model error. Misspecifying the censoring model can also lead to under-coverage.

Fridge: focused fine-tuning of ridge regression for personalize predictions

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08481v1 Announce Type: new Abstract: Statistical prediction methods typically require some form of fine-tuning of tuning parameter(s), with $K$-fold cross-validation as the canonical procedure. For ridge regression there exist numerous procedures, but common for all, including cross-validation, is that one single parameter is chosen for all future predictions. We propose instead to calculate a unique tuning parameter for each individual for which we wish to predict an outcome. This generates an individualized prediction by focusing on the vector of covariates of a specific individual. The focused ridge -- fridge -- procedure is introduced with a two-part contribution: 1) first we define an oracle tuning parameter minimizing the mean squared prediction error of a specific covariate vector, 2) then we propose to estimate this tuning parameter by using plug-in estimates of the regression coefficients and error variance parameter. The procedure is extended to logistic ridge regression by utilizing parametric bootstrap. For high-dimensional data, we propose to use ridge regression with cross-validation as the plug-in estimate, and simulations show that fridge gives smaller average prediction error than ridge with cross-validation for both simulated and real data. We illustrate the new concept for both linear and logistic regression models in two applications of personalized medicine: predicting individual risk and treatment response based on gene expression data. The method is implemented in the R package "fridge".

Covariate-dependent Nonparametric $g$-modeling for regression via infinite Mixture-of-Expertizing class

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08321v1 Announce Type: new Abstract: Empirical Bayes $g$-modeling captures unit-level heterogeneity by estimating a latent prior distribution from observed data. In the existing formulations, however, the prior is shared by all units. In this paper, we develop a covariate-dependent g-modeling framework for regression in which the entire prior distribution of the regression coefficients is allowed to depend on covariates. We formulate the estimation of the prior as nonparametric maximum likelihood estimation (NPMLE) of the covariate-dependent prior, and show that the unrestricted problem is ill-posed. To resolve this, we introduce the infinite Mixture-of-Expertizing class of conditional priors, under which the NPMLE is precisely a softmax-gated Mixture of Experts (MoE) whose number of experts is not fixed in advance but is determined by the data. Building on a first-order optimality condition, we propose two exemplar-based estimation algorithms that select experts automatically, together with a post-hoc aggregation of experts for interpretation. On the theoretical side, we show that every conditional prior in the class is Lipschitz continuous in the covariates, and that aggregated softmax gates can approximate any continuous gate function. The effectiveness of the proposed NPMLE is shown through application to synthetic datasets and real datasets.

Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08292v1 Announce Type: new Abstract: Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study simultaneous inference for local mean contrasts when the number of available diagrams is fixed. They are differences in expected weighted feature mass within $\ell_\infty$ neighborhoods at several centers and radii. We estimate these contrasts using additive landmark responses. A Gaussian multiplier bootstrap calibrates simultaneous confidence intervals while allowing unequal group covariances. The neighborhoods whose intervals exclude zero form a map with approximate family-wise error control, and selecting a subset of original intervals for display preserves their joint coverage guarantee. On the simultaneous coverage event, every reported neighborhood lies within twice its radius of the support of the mean-measure difference. A geometric result gives sufficient radius conditions for a displaced feature to produce a nonzero contrast. A comparison of sufficient detection thresholds quantifies the tradeoff between reducing the number of tested coordinates and reserving observations for an independent pilot. In simulations with 40 to 120 diagrams per class, the bands achieved 94%-98% simultaneous coverage under both the strict null and equal means with unequal covariances. In the latter setting, a permutation maximum and the pooled-t implementation of the two-stage persistence-image test of Moon and Lazar rejected in up to 32% and 26% of runs, respectively. In the fixed-budget simulations, spending a third of the observations on a pilot to choose landmarks or radii located changes less often than a prespecified grid at a single radius. On the MUTAG benchmark, the localized region concentrates on rings of fused-ring systems, an exploratory reading.

The Missing Corner: When Sharp Causal Bounds Fail to Compose

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08197v1 Announce Type: new Abstract: Sharp bounds on two potential-outcome means need not combine into sharp bounds on their difference. We characterize exactly when composition is guaranteed across environments sharing a joint potential-outcome law. For binary treatment and outcome, fix strict selection-probability bounds and interior treatment propensities. Subtracting the full model's sharp mean intervals gives sharp average-treatment-effect bounds for every compatible observed law if and only if the absolute selection bounds coincide across environments. Under this alignment, the complete mean region is rectangular; its endpoints and attaining causal models require $O(K)$ arithmetic operations for $K$ environments. For every mismatch, failure occurs on a relatively open set of positive observed tables at the prescribed propensities and persists under small joint drift. We give computable perturbation certificates and an exact family whose gap is first order in the mismatch. A separate finite-confounding family shows when the lost joint information changes an identified causal sign. These results distinguish local marginal sharpness from joint attainability after combining environments.

TEASE: Targeted elastic spatial envelope

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08157v1 Announce Type: new Abstract: Envelope regression is a crucial part of multivariate linear modeling, leveraging separation into material and immaterial parts to provide parsimonious data reduction. Rekabdarkolaee et al. (2020) construct spatial envelope, a novel multivariate Gaussian process, extended by May et al. (2022) to linear coregionalization envelope. Our proposal (TEASE) combines spatial envelope and full-scale basis graphical lasso (LeDuc et al., 2025), leveraging targeted graphical elastic net (Kov\'acs et al., 2021) for immaterial precision matrices. Material part is a multivariate multiresolution Gaussian Markov random field (Kleiber et al., 2019; Caringi and Secchi, 2026). Enhanced envelope penalty (Kwon and Zou, 2025) regularizes regression coefficients. Demonstrations are on climate data.

What Should We Measure Next? Finding Identification Strategies by Refining Mechanisms

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08092v1 Announce Type: new Abstract: Canonical approaches in causal inference treat model specification as fixed, assuming that researchers directly translate all relevant domain knowledge into a causal model, which can then be used to deduce its logical implications. Yet, in practical applications, model specification is often an iterative process, and involves exploration and introspection: of the many aspects of the phenomenon one could investigate, which ones actually matter for the identification of the causal effect of interest? In this paper we study the problem of iterative identification in partially specified causal models. We focus on determining where observing variables that intercept a direct effect or a confounding path between two variables could enable identification in semi-Markovian models. We give necessary and sufficient graphical conditions for when observing such variables can render an unidentifiable query identifiable, together with an efficient algorithm for locating all such opportunities in a given causal diagram. Our results can help analysts better navigate the model space by drawing attention to the parts of their substantive knowledge that could result in a successful identification strategy.

Collaborative representations for targeted causal inference under outcome selection

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08073v1 Announce Type: new Abstract: Estimating causal effects with missing outcomes requires learning outcome, exposure, and selection models. Flexible propensity learners can predict treatment or missingness well while worsening target estimation by emphasizing instruments, weak-overlap regions, or variation unrelated to outcome-regression bias. We propose a collaborative representation-based targeted learning method for recovered average treatment effects under outcome selection. The method learns low-dimensional exposure and selection representations from cross-fitted pseudo-outcomes that encode outcome-regression drift. A finite candidate library alternates targeted outcome updates with representation updates, and inner cross-validation selects representation complexity, collaboration strength, and regularization using a target-aware risk. We give high-level sufficient conditions for collaborative robustness, consistency, and asymptotic linearity after outer validation-fold targeting. Simulations show finite-sample bias reduction, with explicit bias-variance trade-offs across configurations and relative to competing estimators

Scope-Restricted Backtracking Counterfactuals

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08017v1 Announce Type: new Abstract: Interventional counterfactuals evaluate statements such as "had $A$ been $a$" by replacing the assignment for $A$ while keeping the unit's exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.

Design-Driven Inference for Online Experiments: Jointly Optimal Evidence Collection, Testing, and Estimation

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07831v1 Announce Type: new Abstract: Online multifactorial experiments requires early stopping for practically negligible effects while controlling false stopping under continuous monitoring and retaining precise treatment-effect estimation. We develop a design-driven framework that chooses allocation and the evidence rule jointly, treating allocation as evidence collection and testing and estimation as complementary uses of the same evidence. For multifactor experiments with nuisance block effects and treatment-by-block interactions, we show that block-orthogonal designs remove nuisance contamination from the treatment score and form a complete class for worst-case evidence growth. Under a fixed information budget, an isotropic allocation and an explicit radial e-value jointly attain the minimax rate optimal for directionally unknown alternatives. The same allocation is universally optimal for maximum likelihood estimation of treatment effects, simultaneously achieving A-, D-, and E-optimality and establishing double optimality for testing and estimation. Batchwise replication yields an anytime-valid e-process, retains minimax rate optimality for cumulative conditional worst-case evidence growth, and preserves universal estimation optimality for the prespecified complete experiment. Simulations and a large language model prompt experiment illustrate gains in stopping efficiency and estimation precision.

Measuring Negotiation Traits with Collaborative Choice Data: A Two-Stage Latent Variable Model

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07630v1 Announce Type: new Abstract: Consider a collaborative decision-making setting in which team members with different reward structures need to make a joint decision. Repeated collaborative decisions can reflect individual differences in team members' negotiation ability. However, extracting such information is challenging because each observed response arises from a collaborative process involving multiple participants and their reward structures. In this paper, we propose a two-stage probabilistic measurement model for structured collaborative choice tasks. In the first stage, known member-specific rewards and latent participant negotiation traits jointly determine team-option utilities, from which a latent team choice is generated. In the second stage, individual responses are modeled conditional on the latent team choice, with possible deviations that depend on participants' own rewards. Participant-level covariates can also be incorporated through a structural model. A simulation study shows satisfactory recovery of the participant traits and model parameters across different sample sizes and item sizes. An application to data from simulated collaborative negotiation tasks shows choice prediction accuracy well above the random-choice baseline and meaningful associations between the estimated traits and external criterion variables. The proposed framework provides a psychometric approach to measuring participant-level negotiation traits with collaborative choice data.

Debiased Machine Learning for Count Data: a Partially Linear Poisson Model Based on Neural Networks

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07500v1 Announce Type: new Abstract: We develop a novel debiased machine learning (DML) estimator to analyze count data, which are common in clinical or biomedical studies. Specifically, we estimate the effect of a binary treatment on count outcomes using a partially linear Poisson model. A key advantage of this model is that it represents the complex covariate structure through a nuisance function, which is estimated flexibly using neural networks. We use a Neyman-orthogonal score function to construct the estimator, reducing its sensitivity to errors in estimating the nuisance function. Cross-fitting is used to mitigate overfitting bias in neural networks. Under mild regularity conditions, this DML estimator is asymptotically normal with root-$n$ convergence. We derive a closed-form variance estimator and construct a Wald confidence interval for the treatment effect. Extensive simulations demonstrate that the proposed estimator reduces bias and root mean square error compared with the generalized linear model and the augmented inverse probability weighting (AIPW) estimator in most settings, while achieving a coverage probability near the nominal level. The proposed procedure is implemented in the R package $\texttt{PoissonDML}$. We apply our approach to a synthetic HIV cohort data to investigate the effect of treatment on AIDS-defining event counts of 7,141 analyzed patients. Our approach provides practical and valid estimation and inference for treatment effects under the partially linear Poisson model while combining modern machine learning methods to estimate complex covariate structures.

Large-scale linear hypothesis testing for high-dimensional online M-estimation

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07418v1 Announce Type: new Abstract: With the growing prevalence of streaming data, renewable estimation has become an important tool for updating statistical analyses without retaining historical raw observations. We study estimation and linear hypothesis testing in high-dimensional online M-estimation. Existing renewable procedures based on quadratic approximations can incur first-order approximation errors because the gradient of the unpenalized loss generally does not vanish at a preceding penalized estimator, posing a particular challenge for valid inference. To address this issue, we propose a corrected renewable loss that preserves historical first-order information and combine it with partial folded concave regularization and an iterative local linear approximation. We establish finite sample $\ell_1$- and $\ell_2$-error bounds, together with contraction bounds and strong oracle properties for both the constrained and unconstrained iterative estimators. Building on these results, we derive oracle Bahadur representations and establish asymptotically valid Wald and score tests for general linear hypotheses, allowing both the testing-oracle dimension and the number of restrictions to diverge. We further characterize their asymptotic power under local alternatives. The proposed procedure requires only recursively updated summaries while recovering the first-order inferential behavior of its pooled-data oracle counterpart. Simulation studies and real-data applications demonstrate the finite-sample performance of the proposed estimation and testing procedures.

Multiple Change Point Detection in the Mean and Covariance of High-Dimensional Matrix Time Series

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07392v1 Announce Type: new Abstract: This paper studies simultaneous change point detection in the first- and second-order structures of high-dimensional matrix-valued time series. Specifically, we extend the framework of main effect factor models to accommodate multiple change points so that shifts in the mean and covariance structures are characterized by changes in the trend-stationary main effects main effects and in the factor-driven common components, respectively. Under this framework, the two types of changes are not necessarily aligned and can be arbitrarily large without masking the effects of each other, and each of the detected change points is identified either with the row or column categorizations which improves their interpretability. We propose a unified procedure based on moving-sum statistics to detect and localize both types of changes. Under general regularity conditions that allow for temporal and cross-sectional dependence, we derive detection and localization guarantees for the proposed method. The finite-sample performance of the method is demonstrated through extensive experiments, and its practical usefulness is illustrated by a real data application to New York City Yellow Taxi trip records.

A perspective note on likelihood approximation and inference for complex simulation models using a chain of aggregated normalizing flows

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07391v1 Announce Type: new Abstract: We present a new perspective on the problem of likelihood approximation within the framework of simulation-based inference that promotes scalable and controllable simulation routines for large-scale data analysis, allows efficient parameter space exploration or smooth interpolation in high-dimensions and, thus, supports valid statistical treatments of hypothesis testings as well as uncertainty quantification. In particular, we consider a chain of $n$-aggregated normalizing flows for likelihood approximation scheme, where a set of upfront replicated observation datasets from the forward complex simulation model pass through the first set of bijective transformations, and then subsequently pass to the other sets of bijective transformations. Here, we assume that, for any $k \in \{1,\,2, \ldots, n\}$, the parameters corresponding to the first $k$ sets of bijective transformations are estimated sequentially, in some sense of optimality, for constructing flexible probability distributions, regardless of the remaining $(n-k)$ sets of bijective transformations. Moreover, our objects of interest are to highlight two complementary mathematical arguments that leverage an informatics-theoretic formalization, based-on empirical likelihood estimators under moment restrictions, and a sequential decision-making paradigm, with mixing distributions, for updating and aggregating the estimated parameters of the overall normalizing flows. As a by-product, the framework provides a reliable surrogate model, conditioned on the model parameters defining the forward computational simulation, that allows samples generation, with statistical powers, and facilitates computationally tractable scheme in the Bayesian paradigm for inference, hypothesis testings and uncertainty quantification.

Existence and consistency of weighted maximum likelihood estimator for extreme quantile regression

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07344v1 Announce Type: new Abstract: Estimating extreme conditional quantiles faces two major challenges: understanding complex nonlinear relationships between variables and accurately extrapolating into the tails of the distribution, where data are sparse. To address both issues, we introduce a novel approach that combines the theoretical framework of block maxima with the predictive power of generalized random forests. The conditional distribution of maxima is modeled by a generalized extreme value (GEV) distribution whose parameters depend on the covariates and are estimated via a weighted maximum likelihood procedure, with weights derived from generalized random forests to capture complex high-dimensional structures. The conditional quantile estimator follows from the inversion of the estimated GEV distribution function. We establish theoretical results ensuring the existence and consistency of the proposed weighted maximum likelihood estimator. The method provides a robust and flexible framework for extreme quantile regression. The performance of the proposed approach is illustrated using simulated data, as well as an application to financial portfolio losses from stocks listed on the NYSE, AMEX, and NASDAQ.

Empirical-Bayes spectral partial pooling across related tasks

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07284v1 Announce Type: new Abstract: Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (\texttt{HSS}), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, \texttt{HSS} yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

Deep Time-Series Forecasting in 10 Years: A Survey

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2603.19899v2 Announce Type: replace-cross Abstract: Autocorrelation is a common property of time-series, where each observation is dependent on its predecessors. In deep time-series forecasting, it raises two central challenges: (1) designing backbone architectures to model autocorrelation in history sequences, and (2) devising loss functions to model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper reviews deep time-series forecasting from an autocorrelation modeling perspective, offering two contributions beyond existing surveys. First, it introduces a taxonomy that jointly covers both backbone architectures and loss functions, whereas prior surveys provide limited coverage of the latter. Second, it analyzes the motivations and insights underlying the surveyed literature from a unified autocorrelation perspective, providing a holistic overview of the field's evolution. Additional resources and details are available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Function on Scalar Regression with Complex Survey Designs

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2511.05487v2 Announce Type: replace-cross Abstract: Large health surveys increasingly collect high-dimensional functional data from wearable devices, and function on scalar regression (FoSR) is used to quantify the relationship between these functional outcomes and scalar covariates like age and sex. However, existing methods for FoSR fail to account for complex survey design. We introduce inferential methods for FoSR with complex survey designs. The approach combines fast univariate inference (FUI) developed for functional outcomes and survey sampling inferential methods developed for scalar outcomes. Our approach consists of three steps: (1) fit survey weighted GLMs at each point along the functional domain, (2) smooth coefficients along the functional domain, and (3) use balanced repeated replication (BRR) or Rao-Wu-Yue-Beaumont (RWYB) bootstrap to obtain pointwise and joint confidence bands for the functional coefficients. The approach is motivated by association studies between continuous physical activity data and covariates collected in the National Health and Nutrition Examination Survey (NHANES). A first-of-its-kind analytical simulation study and empirical simulation using NHANES data demonstrates that our approach performs better than existing methods that do not account for the survey structure. Finally, application of the approach in NHANES shows the practical implications of accounting for survey structure. The approach is implemented in the R package \texttt{svyfosr}.

FreDF: Learning to Forecast in the Frequency Domain

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2402.02399v3 Announce Type: replace-cross Abstract: Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

Second-Order Response Laws for LLM Judges: Debiased Estimation of Prompt Instability

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2608.16253v2 Announce Type: replace Abstract: LLM judges are often evaluated with a single prompt and only a few repeated calls. When their verdicts vary, it remains unclear whether the variation comes from sampling noise within a prompt or systematic differences across prompts. We formalize this distinction using a second-order response law: the distribution of prompt-conditioned verdict distributions induced by a declared prompt policy. For a quadratic measure of prompt instability, we show that the usual plug-in estimator is biased upward at finite repeat budgets because it confounds within-prompt noise with between-prompt variation. We derive unbiased estimators for both sampled prompts and declared fixed prompt censuses from the difference between within- and across-prompt agreement. Under a crossed prompt-by-answer-order design, the same framework separates prompt, order, interaction, and residual call variation, while retaining invalid completed outputs as outcomes. Known-law simulations and a byte-identical live null recover the predicted finite-$R$ inflation. In a matched Qwen study, corrected low-repeat estimates are closer to an independently acquired $R=16$ reference than plug-in estimates, with the largest gains at small repeat budgets. A matched panel across four frozen judge configurations exhibits configuration-specific inflation magnitudes and component profiles. Prompt robustness can therefore be estimated separately from finite-call noise.

Stable Multivariate Functional Time Series Prediction for Major Geomagnetic Indices

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2606.14417v2 Announce Type: replace Abstract: High-resolution scientific data, such as geomagnetic index streams, often exhibit complex temporal dependencies that can be modeled through functional data analysis. Conventional functional time series (FTS) methods typically partition continuous processes into non-overlapping segments, which artificially fragments temporal continuity and can limit estimation efficiency and stability. This is particularly evident in geomagnetic time series prediction due to their noisy, sudden, and large-scale changes. This study presents a robust multivariate FTS forecasting framework for multi-dimensional time series with inter-series correlations and the existence of exogenous predictors. We introduce an overlapping rolling-window scheme that preserves temporal coherence and mitigates boundary information loss, thereby enriching the effective sample size for a more efficient and stable estimation. We integrate functional principal component analysis for dimension reduction with a vector autoregressive model with exogenous inputs to capture latent dynamics across correlated series. We also construct computationally efficient conformal prediction intervals for uncertainty quantification. The framework is motivated by and applied to the simultaneous forecasting of five critical geomagnetic indices, Kp, Dst, SYM-H, SME, and SMR, using solar wind parameters as predictors. Empirical results show that this approach outperforms state-of-the-art machine learning baselines, extends forecast horizons to 6-24 hours, and provides calibrated uncertainty bounds.

DRtool: An Interactive Tool for Analyzing High-Dimensional Clusterings

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2509.04603v4 Announce Type: replace Abstract: When faced with new data, we often conduct a cluster analysis to obtain a better understanding of the data's structure and the archetypical samples present in the data. However, the increases in data complexity and dimensionality have made this step very tricky. The large proportion of noise in high-dimensional data blurs patterns and trends, making clusters difficult to distinguish. As such, cluster-discovery tools and cluster-verification tools must be adapted to address the difficulties of high-dimensional data. Nonlinear dimension reduction is a step in the right direction, but even these methods are known to produce false structures, especially when mishandled. A common phenomenon that often goes undetected by the untrained eye is over-clustering of the data. In continuation of these efforts, we developed new cluster verification techniques, including visual assessments and a hypothesis test, that help analysts distinguish false clusters and better interpret their high-dimensional clustering results. For ease of use, these new methods are provided in an interactive toolbox available via R package DRTool.

Walking Fingerprinting Using Wrist Accelerometry During Activities of Daily Living in NHANES

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2506.17160v2 Announce Type: replace Abstract: We propose a method for identifying individuals based on their continuously monitored wrist-worn accelerometry during activities of daily living. The method consists of three steps: (1) using Adaptive Empirical Pattern Transformation (ADEPT), a highly specific method to identify walking; (2) transforming the accelerometry time series into an image that corresponds to the joint distribution of the time series and its lags; and (3) using the resulting images to construct a person-specific walking fingerprint. The method is applied to 15,000 individuals from the National Health and Nutrition Examination Survey (NHANES) with up to 7 days of wrist accelerometry data collected at 80 Hertz. The resulting dataset contains more than 10 terabytes, is roughly 2 to 3 orders of magnitude larger than previous datasets used for activity recognition, is collected in the free living environment, and does not contain labels for walking periods. Using extensive cross-validation studies, we show that our method is highly predictive and can be successfully extended to a large, heterogeneous sample representative of the U.S. population: in the highest-performing model, the correct participant is in the top 1% of predictions 96% of the time.

Scalable Regularized Vector Multiplicative Error Models for Positive-valued Financial Time Series

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08443v1 Announce Type: cross Abstract: The logarithmic multiplicative error model (log-vMEM) has been useful in modeling and forecasting multivariate positive-valued financial time series. The number of parameters grow rapidly with the dimension of the system and the lag order, making estimation computationally demanding in high-dimensional settings. This paper describes regularized estimation via hierarchical lag structures (Nicholson et al., 2020) for log-vMEM models with multivariate gamma error distribution of Tsionas (2004). The parameter estimation is performed using a blockwise coordinate descent algorithm with a Gauss-Seidel-style update scheme (Wright, 2015). This enables an efficient computation strategy compared to traditional penalized maximum likelihood approaches. The competing models are juxtaposed against each other by combining three hierarchical lag structures (componentwise, elementwise, own-other) and four penalties(group-lasso, adaptive group-lasso, group-mcp, and group-scad). Extensive simulation runs have been performed to test the parameter recovery for both the unpenalized and the penalized models. We apply the proposed methods to model the joint dynamics of robust intraday realized volatility measures for Microsoft (NASDAQ: MSFT) for the competing models. The numerical integration step of the log-likelihood is identified to be the principal computational bottleneck. We address this issue by using GPU-accelerated quadrature integration thus improving computational scalability of the proposed models.

Elastic kernel Ridge regression, with applications in phonetics

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08386v1 Announce Type: cross Abstract: Predicting the shapes of entire curves requires accounting for nonlinear geometry and unknown alignments between curves. We develop elastic kernel ridge regression, a nonparametric method for planar curve responses with scalar, multivariate, or functional covariates. Using square-root velocity representations, we formulate penalized conditional Fr\'echet mean estimation in a shape space invariant to translation, rotation, scaling, and reparametrization. A vector-valued reproducing kernel Hilbert space provides a flexible nonlinear link through the spherical exponential map. We use an alternating algorithm to align each observed curve to its current fitted value, and updates the regression function. To facilitate this, we provide a new Euclidean quasi-Newton solver that exploits scale invariance of the reparametrization objective; this accelerates alignment while retaining accuracy in a numerical comparison. Simulations demonstrate the benefits of estimating alignment within the regression and respecting spherical geometry. Applied to vocal tract contours from a real-time magnetic resonance imaging recording, the method recovers missing frames and reconstructs shape trajectories from downsampled data. A speech inversion proof of concept on the same recording predicts tongue shapes from acoustic features, illustrating the method's potential. The method is implemented in the \texttt{R} package \texttt{sphereg2}.

Bayesian heterogeneous copula mixtures with nonparametric margins: consistency, identifiability and tail asymmetry in physical fitness data

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08317v1 Announce Type: cross Abstract: Finite mixtures of Clayton, Gumbel, Frank and Gaussian copulas can describe dependence that differs between the upper and lower tails. We study a two-stage Bayesian analysis in which ranks or kernel estimates replace the margins and the copula likelihood is evaluated at the resulting pseudo-observations. This pseudo-posterior is strongly consistent for the copula density whenever the log density admits a logarithmic boundary envelope. Both stages may use the same data, margins may be standardized within observed strata, and neither smoothness nor identifiability is required. The envelope holds for finite mixtures of Gaussian, Student, Clayton, Gumbel and Frank copulas in any fixed dimension; tail-dependence coefficients and conditional tail probabilities are therefore consistently estimated. We further prove that Clayton, Gumbel, Frank and Gaussian copulas are jointly finitely linearly independent, which makes mixture weights and components identifiable and consistently estimated. In simulations the pseudo-posterior matches multi-start maximum pseudo-likelihood in large samples. It is more stable in small samples and near independence (every component close to the independence copula), where tail coefficients are learned long before the weights and a marginal Metropolis sampler is up to twice as efficient as data augmentation. Two physical fitness datasets show mirror-image asymmetries. Among 8772 university students, sprint and jump performance are coupled mainly at the top. Among 5336 adults in a national health survey, low grip strength and low daily activity cluster together, increasingly with age, whereas high values do not. A Gaussian copula misses both patterns in held-out data.

The Topp-Leone XLindley Distribution: Properties, Estimation and Applications to Lifetime Data

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08059v1 Announce Type: cross Abstract: In this article, we use a family of distributions developed by Topp-Leone to create a novel lifetime two-parameter distribution. The Topp-Leone XLindley distribution is the name used for it. We study several types of statistical and mathematical characteristics of this distribution, such as reliability functions, moments, moment-generating function, quantile function, and the Renyi entropy. For the purpose of estimating parameters under the proposed distribution model, this simulation study is conducted to evaluate the performance of the maximum likelihood estimates for the parameters of the Topp-Leone XLindley distribution. A comprehensive simulation investigation is carried out to evaluate the performance of the proposed methods. Furthermore, a practical data set of bank customer waiting times has been investigated for the purpose of illustration.

State-space representation of early-life child mortality dynamics: linking event history analysis and orbit-based models

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07877v1 Announce Type: cross Abstract: Understanding early-life child mortality requires methods that capture both statistically significant risk factors and the structure of individual life trajectories. Event History Analysis (EHA) estimates associations between covariates and mortality risk but may obscure rare or high-dimensional configurations of risk. Orbit Theory (OT) represents individuals as exact trajectories in a combinatorial state space, preserving full multivariate structure. We analyse longitudinal data across 12 variables for 31,081 children from the Agincourt Health and Demographic Surveillance System (South Africa, 1998-2008) using both methods. We show three things EHA alone cannot. First, maternal migration is structurally pivotal in the transition dynamics leading to child death despite being statistically non-significant in EHA. Second, maternal refugee status, while statistically significant, generates no trajectory dynamics and is correctly excluded from any structural reduction. Third, a three-variable subsystem (child status, mother status, mother migration) recovers EHA's principal findings within a reduced state space of at most 48 states while exposing small high-risk clusters invisible to regression-based analysis. Maternal death is the dominant EHA predictor; maternal migration organises 87% of the observable sequential transitions into child-death states. These are not contradictory: maternal death rarely appears as a preceding state because its role is terminal rather than sequential. Early-life mortality can be read at two levels simultaneously - statistically, through effect estimates, and structurally, through observed transitions.

Trustworthy Method Comparison with AI Judges: Estimation and Design under Order, Batch, and Aggregation Effects

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07755v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used as judges for automated AI evaluation. A common practice is to randomize prompt sequences and average the resulting scores, but its statistical validity remains unclear. We show that LLM evaluation mechanisms can be approximated by a class of Markov generalized linear mixed models (GLMMs), supported by out-of-sample predictions across three major commercial LLMs. Using a first-order Markov GLMM, we study leaderboard ranking and group comparison. For leaderboard ranking, randomize-and-average selection is consistent under a mild separation condition, and a Williams square design can improve efficiency when item qualities are close. For group comparison, naive averaging can yield inconsistent conclusions about differences in group-level quality because of the response model's nonlinearity. Empirical results further support the validity of the proposed model-based inference beyond the first-order theory, including settings with higher-order sequence memory. We illustrate the approach in an application where AI judges compare two graphical model estimation methods.

Active Feature Acquisition for Cost-Efficient Temporal Prediction with Reduced Participant Burden

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07452v1 Announce Type: cross Abstract: Accurate forecasting of pathological outcomes is a central problem in psychology. To do so, psychologists often collect intensive longitudinal data. However, in such studies, the desire to acquire a large number of variables for the sake of accurate prediction is often counteracted by the need to minimize participant burden. Acquiring more variables per occasion can yield better predictions, but having too many acquisitions increase the risk of non-response and attrition. Longitudinal Active Feature Acquisition (LAFA) is a principled approach to resolve this conundrum. Instead of requiring responses to every item at every acquisition occasion, LAFA produces a policy that seeks to optimally select dynamic subsets of items to be acquired at each timepoint while preserving our ability to forecast a specific outcome. However, existing LAFA methods are mostly based on Neural Networks (NN) that are difficult to interpret in practice. In this work, we introduce a tree distillation method for learning an interpretable policy from NN-based LAFA networks. We validated our method through both a simulation and an empirical EMA dataset on forecasting daily alcohol consumption. In both cases, we find that we can meaningfully reduce the number of items acquired at each occasion with minimal loss in accuracy. Networks (NN) that are difficult to interpret in practice. In this work, we introduce a tree distillation method for learning an interpretable policy from NN-based LAFA networks. We validated our method through both a simulation and an empirical EMA dataset on forecasting daily alcohol consumption. In both cases, we find that we can meaningfully reduce the number of items acquired at each occasion with minimal loss in accuracy.

HyperNSDE: Personalized Neural SDEs for Joint Static-Longitudinal Clinical Data Generation

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07383v1 Announce Type: cross Abstract: Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learning. Realistic synthesis of patient-level clinical data requires jointly modeling heterogeneous static covariates, irregularly sampled longitudinal trajectories, and informative observation times - three tightly coupled components in practice yet rarely addressed together. We propose HyperNSDE, a continuous-time generative model that conditions a latent Neural SDE on static patient representations through a hypernetwork, allowing baseline characteristics to shape trajectory evolution beyond the initial condition without requiring a trajectory encoder, while stochastic latent dynamics capture realistic variability in generated paths. Observation times are modeled jointly through a latent-state-dependent intensity process, and training on irregular stochastic paths is stabilized via a deterministic-stochastic path decomposition with a non-adversarial signature-kernel objective. Experiments on simulated and real clinical datasets show improved observation-time fidelity and competitive performance, while matched-grid analyses reveal that forecasting and correlation metrics are affected by observation-grid regularity and trajectory smoothness.

lifelines-hc: Higher Criticism testing for sparse non-proportional hazard departures in Python

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07268v1 Announce Type: cross Abstract: The log-rank test is the standard tool for two-sample survival comparison and has good power against proportional-hazards alternatives, but it loses power against sparse hazard departures, in which the hazard difference is concentrated in a small number of time intervals whose locations along the follow-up are unknown a priori (Kipnis, Galili and Yakhini, Biometrika 2026). Weighted log-rank tests -- Gehan-Wilcoxon, Tarone-Ware, Peto-Prentice, Fleming-Harrington -- each impose a pre-specified temporal emphasis. Combination procedures such as MaxCombo and the Yang-Prentice short-term/long-term hazard-ratio model relax that choice, but still scan only a small dictionary of global temporal shapes and remain insensitive to sparse departures occurring outside them. We introduce lifelines-hc, a Python package extending the lifelines survival library with the HCHG test: Higher Criticism applied to per-interval hypergeometric p-values. HCHG applies to right-censored two-sample data and detects sparse hazard departures at unknown locations without committing to any temporal pattern. Across four clinical case studies -- CheckMate 057 PFS (n=582), COMET-1 OS (n=1028), AZURE DFS (n=3359), and the Copenhagen Study Group for Liver Diseases cirrhosis trial (n=446, fully public individual patient data) -- HCHG achieves p = 0.26). MaxCombo and the Yang-Prentice adaptive log-rank test detect the delayed-benefit crossing in CheckMate 057 (p = 0.24), where the departure is sparse or multi-window rather than a smooth short-term/long-term hazard-ratio pattern. lifelines-hc is freely available under the MIT license at https://github.com/alonkipnis/lifelines-hc and via pip install lifelines-hc.

A Bayesian Multiscale Integrated Abundance Model for Estimating Latent Opioid Misuse Prevalence from Spatially Misaligned Data

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07265v1 Announce Type: cross Abstract: Estimating small area prevalence of opioid misuse is critical for targeting public health interventions, yet direct measures are unavailable and related surveillance data are often reported on misaligned areal units. We propose a Bayesian Multiscale Integrated Abundance (MIA) model for estimating latent opioid misuse prevalence by jointly analyzing multiple indirect surveillance indicators observed on different geographic supports. The model extends existing integrated abundance models by representing all source geographies through a common set of atomic spatial units formed by the intersections of observed areal supports. Latent prevalence at the atomic level is modeled using a Fisher noncentral hypergeometric distribution, which preserves county-level prevalence totals while respecting local population constraints. To enable scalable inference, we develop a two-stage compositional Markov chain Monte Carlo algorithm that combines customized sampling strategies and parallel computing. Simulation studies show the proposed approach reduces bias and root mean squared error relative to common downscaling methods. We apply the model to Ohio data from 2010-2023, integrating state-level survey estimates, county-level counts of opioid overdose deaths and treatment admissions, and ZIP code tabulation area-level counts of emergency medical services naloxone administrations. Results reveal substantial within-county heterogeneity and identify localized areas of elevated opioid misuse prevalence that would be missed by county-level analyses.

A Data-Driven Framework for Unsupervised Monitoring of Transmission Systems Using End-of-Line Testing Data: A Case Study at Ford Motor Company

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.06980v1 Announce Type: cross Abstract: Sensing technologies have advanced rapidly across industries ranging from energy to automotive manufacturing. These systems generate high-dimensional (HD) data characterized by complex nonlinear patterns and strong temporal dependencies. Traditional statistical monitoring methods are often limited in their ability to capture such nonlinear structure. Likewise, many analytical approaches used in End-of-Line testing rely on predefined thresholds and heuristic rules, which restrict their ability to detect informative anomaly signatures in HD temporal data. In contrast, while modern deep learning and generative AI models offer strong predictive capabilities, they are often unsuitable in applications where data are costly to collect and where the monitoring system must remain interpretable, low-latency, computationally efficient, and usable by non-technical practitioners. To overcome these limitations, we propose an advanced multivariate monitoring framework for HD data. The framework operates in two stages. In the first stage, the data are preprocessed to remove incomplete and non-informative samples and to temporally align time series data. In the second stage, nonlinear dimensionality reduction is performed, followed by anomaly detection through a control chart based phase I monitoring procedure. The framework can be used in both unsupervised and supervised settings, depending on the availability of ground truth labels during training. Moreover, its flexible and modular structure allows practitioners to adapt its components to different domains and operational requirements. We evaluate the proposed framework on real production data from an automotive manufacturing environment at Ford Motor Company. The proposed method achieves higher accuracy, recall, and F1 score than the company's existing model, improving these metrics from 0.50, 0.30, and 0.429 to 0.625, 1.00, and 0.769, respectively.

Low-Rank and Structured Sparse Tensor Decomposition for Anomaly Detection in Multivariate Functional Data

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.06930v1 Announce Type: cross Abstract: Multivariate functional data arise in many modern manufacturing systems, where multiple sensors record densely sampled process trajectories. Monitoring such data is challenging because nominal variation is strongly correlated across samples, sensors, and time, while faults may appear either as isolated deviations or as structured departures concentrated within a limited number of sensor-specific temporal trajectories. We propose two unsupervised sparse tensor decomposition methods that preserve this multimode structure. Entrywise Sparse CP Decomposition (ES-CP) uses an entrywise $\ell_1$ penalty to identify localized anomalies, whereas Fiberwise Sparse-Group Lasso CP Decomposition (FG-Lasso) combines entrywise and fiberwise penalties to detect both localized deviations and anomalies concentrated within temporal fibers. Both methods represent nominal process behavior through a low-rank CP decomposition and are estimated using alternating optimization with closed-form sparse-component updates. Two simulation studies evaluate performance under different fault structures, signal severities, noise levels, and missing observations. FG-Lasso attains or ties the highest macro F$_1$ score in almost all settings in the first study and achieves the highest macro F$_1$ score. In a multichannel forging-process case study, FG-Lasso and ES-CP obtain macro F$_1$ scores of 0.85 and 0.82, respectively, compared with 0.69 or lower for TRPCA and PCA-based anomaly detectors. The results demonstrate that explicitly matching the sparse penalty to the anticipated fault structure improves both anomaly detection and fault localization in high-dimensional functional processes.

FireGen: Quantifying Wildfire Risk by Simulation

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07431v1 Announce Type: new Abstract: Wildfire regimes in Northern California exhibit strong spatio-temporal variability, heavy-tailed fire size distributions, and sensitivity to climatic conditions. We develop a hierarchical statistical framework to model wildfire occurrence, geometry, and burned area in Northern California from 1984-2023. Fire centroids are modeled as a spatio-temporal point process with covariate-driven intensity, extended by a multiplicative gamma-based stochastic shock to better capture the distribution of monthly fire counts. Conditional on fire location, burned area polygons are represented using a parametric ellipse model that separates scale, shape, and orientation, with ellipse parameters estimated from standardized fire perimeters. Total burned area is modeled using a heteroskedastic lognormal regression incorporating climatic and spatial covariates, including vapor pressure deficit anomalies. The framework enables Monte Carlo simulation of wildfire processes and provides a probabilistic tool for assessing wildfire risk and cumulative burned area under observed climate variability.

Data Fusion for Errors-in-Variables

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07048v1 Announce Type: cross Abstract: We study errors-in-variables problems in which a target study contains only a single error-prone surrogate of an unobserved exposure, while an external source study provides repeated surrogate measurements from a different population. The measurement error distribution is allowed to depend on the observed error-free variables, and the error-free variable distribution itself may differ between studies. We introduce a conditional transportability assumption that enables the use of external repeated measurements under source-target heterogeneity. Together with additional replicate-error conditions, it identifies the target conditional measurement-error distribution. Building on this identification result, we develop a data-fusion estimator for a broad class of target functionals. The estimator combines conditional deconvolution, flexible nuisance estimation, and orthogonal correction that reduces first-order sensitivity to nuisance estimation. For the proposed estimator, we develop a unified spectral theory covering both diffuse-spectrum and finite atomic-spectrum target functionals, derive a general asymptotic expansion, and establish consistency and target-specific convergence-rate bounds. The resulting convergence-rate bounds depend jointly on the spectral properties of the measurement error, the latent exposure, and the target functional. For finite atomic-spectrum targets, we further establish joint Gaussian and bootstrap limits, yielding inference for smooth moment transformations under an additional centering condition. In the reported simulations, Fuse-EIV has small bias for the primary exposure-related coefficient. Applications to the National Health and Nutrition Examination Survey illustrate how accounting for population heterogeneity and error heteroscedasticity can change empirical conclusions.

Anytime-valid simulation-based hypothesis testing

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08210v1 Announce Type: cross Abstract: For a given data distribution $(X_t)_{t \in \mathbb{N}} \sim Q$ i.i.d., we investigate the hypothesis testing problem: $H_0: Q = P_0$ vs. $H_1: Q = P_1$, for two different model probability distributions $P_0$ and $P_1$. In contrast to the standard setting, where analytic densities $p_0$ and $p_1$ are given, here, we consider the density-free setting, where we only have access to i.i.d. simulations $(Z^0_t)_{t \in \mathbb{N}} \sim P_0$ and $(Z^1_t)_{t \in \mathbb{N}} \sim P_1$. For this simulation-based hypothesis testing setting, we construct an e-test martingale, resulting in a sequential test with anytime-valid type-I error guarantees, approximate growth optimality, geometrically decaying type-II error bounds, and asymptotic power one. Most ingredients used in our constructions are variants of well known concepts. The value of this paper lies in the compact presentation of an effective, anytime-valid solution for the density-free simulation-based sequential hypothesis testing case.

Efficient Posterior Sampling for $\mathbb Z_2$ Synchronization

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08199v1 Announce Type: cross Abstract: Consider the $\mathbb Z_2$ synchronization problem \[ \boldsymbol{Y} = \frac{\lambda}{\sqrt n} \theta\theta^{\top} + \boldsymbol{Z}, \] where $\theta$ is uniform on $\{-1,1\}^n$ and $\boldsymbol{Z}$ is an independent Gaussian Wigner matrix with off-diagonal variance one. We give a polynomial-time posterior sampling algorithm for every fixed $\lambda>1$, for which the conditional output law converges to the posterior in total variation, in expectation over the observation. The construction combines sequential TAP proposals with an independence Metropolis correction. The key is to control signed overlaps after logarithmic pinning and conditional TAP approximations along a random revealing path, which give an efficiently evaluable proposal with a polynomial density-ratio bound outside a set of vanishing posterior mass. To the best of our knowledge, this is the first polynomial-time posterior sampler for $\mathbb Z_2$ synchronization with a total-variation guarantee throughout the supercritical regime. For comparison, the diffusion-based sampler of \cite{montanari2023posterior} gives normalized Wasserstein guarantees at sufficiently large fixed signal-to-noise ratio.

The Geometry of Existence and Uniqueness of Maximum Likelihood Estimation in Categorical Response Models

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08100v1 Announce Type: cross Abstract: Nonexistence of the maximum likelihood estimate (MLE) under separation is treated as a solved problem for binary logistic regression and as a scattered collection of model-specific results everywhere else. We show that it is one phenomenon with one criterion. In a latent polyhedral categorical response model, every observed outcome corresponds to a polyhedral event in latent variables whose faces shift linearly with the parameter. Random-utility choice, cumulative-link, ranking, multivariate binary and ordinal, sequential, adjacent-category logit, and fixed-score stereotype models belong to this family. The likelihood sees each observed factor only through the columns of its threshold map, the structure vectors. A finite MLE exists if and only if the pooled structure vector set has overlap. Sufficiency requires only continuity, necessity requires only strictly threshold-increasing probabilities, and neither likelihood concavity, exchangeability, nor full design rank is needed. Positive strictly log-concave latent densities and threshold-identifiable polyhedra then yield uniqueness on the estimable span. A single linear program determines whether overlap holds, and convex cone geometry measures the dimension of separation. An application using cumulative-link models for willingness to share health data identifies observations and model terms associated with nonexistence and illustrates how the diagnostics inform model revision and sensitivity analysis.

Detecting a Shift Is Not Enough: Exact Minimax Limits of Linear Representation Repair

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08069v1 Announce Type: cross Abstract: A mean shift between two data sources can be easy to detect but hard to remove without substantially changing their representations. We cast its removal as a statistical decision problem: from noisy differences between paired calibration measurements in $\mathbb{R}^d$, learn one linear map, applied to both sources under a hard distortion budget, that leaves as little of the shift as possible on fresh data. We derive the exact finite-sample minimax risk over all such maps, $(d-k) \mathbb{E}[1/(d+2J)]$ with $J\sim\mathrm{Pois}(\kappa/2)$, where the budget allows deleting $k$ directions and $\kappa$ is the calibration signal-to-noise ratio. Projecting out the mean calibration difference attains it without knowing $\kappa$ or the noise scale. This exposes a detection-repair gap: detecting the shift needs only $\kappa\gg\sqrt d$, whereas removing a fixed fraction of it at constant distortion needs $\kappa\asymp d$, as for estimating its direction. Standard linear concept erasers (MP, SAL, LEACE) remove the same calibration difference, so the formula gives, before fitting, exactly how much shift they leave on fresh data and how much calibration a target requires. The limit is robust: pairing keeps it exact for non-Gaussian shared content, the projection keeps its guarantee under anisotropic noise, and selective abstention cannot close the gap. On paired clinical and wearable sleep EEG, where differences between participants act as calibration noise, the formula predicts the device shift left in new participants, and more recordings per person soon stop helping. Together, these results tell whether a correction that falls short needs a better method, more recordings, or more participants.

Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07637v1 Announce Type: cross Abstract: Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture this behavior, yet evaluating learning performance under them remains challenging because rare, large feature entries retain non-vanishing effects even in high dimensions. Even in the canonical setting of empirical risk minimization for linear regression with entry-wise i.i.d. symmetric $\alpha$-stable data, a precise asymptotic characterization of prediction has been lacking. In this work, we introduce a functional order parameter that describes the random effective problem associated with each coefficient. Using the replica method, we fully characterize the generalization error in the proportional high-dimensional limit where the sample size and feature dimension diverge at a fixed ratio. Additionally, this analysis establishes a heavy-tail universality law, scaling laws relating typical errors to prediction reliability, and the Bayes-optimal prediction error. In addition to characterizing the effects of extreme entries on the learning process, our method applies broadly to other systems with persistent local heterogeneity.

Endpoint-Stable Interval Inverse Inequalities for Multiscale Kernels with Positive Exponential Spectra

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07612v1 Announce Type: cross Abstract: Inverse inequalities are essential for controlling derivative growth and ensuring stable sampling in kernel approximation. Existing whole-space and single-scale estimates provide an established analytical basis, but their extension to multiscale analytic spaces on finite intervals requires uniform control of boundary effects and cross-scale cancellation. This paper establishes unweighted interval $L^2$ inverse inequalities for spaces generated by primitives of kernels with positive exponential spectra. By retaining exterior diagonal energy and controlling off-diagonal interactions through one-sided estimates with endpoint-distance weights, we derive uniform coefficient bounds for normalized high derivatives. A synthesis-operator perturbation argument extends these bounds to positive spectral mixtures, while adjacent-derivative comparison and interval interpolation yield an inverse bound of order $h_*^{-1}$, where $h_*$ is the smallest scale. Under geometric scale separation and within-scale centre separation, the constant is independent of the number of scales and centres and their distances from the endpoints, allowing endpoint centres and coincident centres across scales. The coefficient lower bound approaches the optimal limit $1/2$. Two-centre constructions establish the sharpness of the scale exponent for every fixed kernel in the class and, for a single exponential spectrum, a sharp deficit of order $q^{-1/2}$ from $1/2$ for the best uniform coefficient lower bound, where $q$ is the derivative order. Numerical illustrations for Cauchy and logistic kernels demonstrate coefficient stability in several multiscale configurations. These results extend interval inverse estimates to multiscale analytic kernel spaces with endpoint centres and provide quantitative conditions for deterministic sampling stability.

Vine Copula VAR:From Recursive Margins to Joint Forecast Inference

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07589v1 Announce Type: cross Abstract: Joint-event forecasts often combine a dependence estimate based on past forecast errors with newly estimated marginal distributions. When each historical error retains the marginal fit available at its issue date, inference must account for an overlapping sequence of estimation errors. We derive their joint influence with the terminal forecast estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical correction to harmonically weighted innovation moments, while terminal slope uncertainty remains. The resulting covariance estimator gives asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. In the Gaussian submodel, retaining issued transforms adds a positive semidefinite covariance term relative to refitting margins on the same observations. Monte Carlo simulations show that terminal-margin uncertainty is quantitatively more important than this additional term and that logit intervals improve lower-tail coverage in the designs studied. A real-time forecasting application to U.S. macroeconomic releases shows how marginal estimation contributes to uncertainty in predicted probabilities of joint contractions and identifies limitations of the stationary marginal model.

Assumption-lean logistic regression with missing covariates

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07292v1 Announce Type: cross Abstract: Missing covariates are frequently encountered in supervised learning problems, and classical methods for estimation using such data use carefully chosen imputation schemes for missing data, or likelihood approximations that lead to nonconvex $M$-estimation problems. These methods and their relatives are suitable for scenarios in which the covariate distribution is known, and more broadly, have enjoyed tremendous success in linear models. But even in basic nonlinear problems such as logistic regression in moderate dimensions, such methods can experience drastic failure modes when the covariate distribution is unknown. Motivated by the need for reliable alternatives, we consider the problem of parameter estimation in logistic regression with missing covariates. Crucially, we operate in the assumption-lean setting where the covariate distribution is unknown (but bounded). We design a stochastic approximation method that is based on $Z$-estimation with a novel monotone operator, and establish that our algorithm is computationally efficient and achieves provable signal recovery at parametric rates under the hypothesis that covariates are missing completely at random. Our theory sharply characterizes the $\ell_2^2$ risk of the estimator in terms of the missingness profile, accommodating heterogeneous observation probabilities. Importantly, it shows that our method always outperforms the de facto ``complete-case'' estimator that ignores observations with any missing data. Even in the setting with homogeneous missingness (in which each covariate is observed independently with probability $q$), our bounds exhibit intricate and nonstandard dependence on $q$ that can yield significant improvements over using only complete cases. We complement our upper bounds with new information-theoretic lower bounds that show that this intricate dependence on $q$ is fundamental in a minimax sense.

Poisson empirical Bayes estimation of sums of random variables via minimum-distance methods

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07190v1 Announce Type: cross Abstract: The estimation of sums of functions of observable and unobservable variables is a long-standing problem in statistics, with applications in many domains. We consider this problem in Poisson mixture models, where empirical Bayes provides a natural framework but nonparametric theory remains limited. We develop a nonparametric empirical Bayes methodology based on regular and coarsened minimum-distance estimation of the unknown mixing distribution. For a broad class of such sums, we establish large-sample guarantees showing that the resulting plug-in estimates asymptotically merge with the oracle Bayes estimate. In particular, when the mixing distribution has finite support, we obtain a nearly parametric convergence rate, up to a logarithmic factor. We then provide a finite-sample analysis of two representative sums: the total intensity among units whose observed count does not exceed a fixed threshold, and the number of units whose observed count exceeds their latent intensity. For the total-intensity sum, we establish a lower bound on the minimax regret and derive upper bounds for both regular and coarsened minimum-distance procedures under compact-support and subexponential assumptions on the mixing distribution. These upper bounds match the minimax rate up to logarithmic factors, with the coarsened procedure in the compact-support setting matching the rate exactly when the coarsening level is fixed. The above-average sum displays a markedly different behavior: a lower bound on the minimax regret shows that bounded regret is in general impossible to achieve. We identify additional stability conditions under which bounded regret can be recovered up to logarithmic factors, and show that these conditions are automatically satisfied when the mixing distribution has finite support. Numerical experiments on both synthetic and real data illustrate the performance of the proposed methodology.

Sample-Optimal Estimation of the Fr\'echet Inception Distance

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07114v1 Announce Type: cross Abstract: The Fr\'echet Inception Distance (FID) is widely used to evaluate generative models, but its empirical plug-in estimator suffers from finite-sample bias [BSAG18, CF20]. We study the sample complexity $n$ of estimating FID to error $\epsilon$ between $d$-dimensional Gaussians with bounded mean distance and covariances, when one distribution is known. Our contributions are threefold. (1) We establish tight finite-sample $\Theta(\frac{d^2}{n})$ bias and $\Theta(\frac{d}{n} + \frac {d^2} {n^2})$ variance bounds for the empirical plug-in estimator, establishing a $\gtrsim d^2$ sample complexity. (2) To debias the empirical plug-in estimator, we generalize the ${\rm FID}_\infty$ estimator of [CF20] to extrapolation methods of arbitrary order $k$. We further prove tight bias and variance bounds of $\Theta(\frac{d^{k + 2}}{n^{k + 1}})$ and $\Theta(\frac d n + \frac{d^2}{n^2})$ for any order-$k$ extrapolation under our framework. (3) We introduce Relative Taylor Debiasing (RTD), a new, computationally efficient FID estimation algorithm using debiasing techniques inspired by U-statistics. We show that RTD achieves an $O(\frac d {\epsilon^2})$ sample complexity, and prove that this is optimal. We provide a complementary empirical evaluation of our new estimators. Our experiments on synthetic Gaussians validate the predicted residual bias and support the tightness of our bounds. On ImageNet with Inception embeddings, RTD achieves the lowest mean estimation error at the standard 50K sample budget, while our second-order variance-aware extrapolation estimator (VALE$_2$) uses only 10K samples to achieve accuracy comparable to FID$_\infty$ at 50K samples.

Asymptotic Null Distributions of Moran's $I$ and Assortativity in Large Networks

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08711v1 Announce Type: new Abstract: This study investigates the asymptotic behavior of two dependence measures defined on networks, Moran's $I$ statistic and Newman's assortativity, under the null hypothesis that a Gaussian node attribute $Y$ is independent of the network structure. We demonstrate that the structure of the network directly affects the convergence rate to normality of these measures as the size of the network increases. We further establish that, in some instances, the mean values of these dependence measures under the null hypothesis remain non-negligible asymptotically and must therefore be explicitly accounted for when calculating the test statistics. Applications to a variety of simulated and real networks also reveal that the normal approximation performs well only when the network is not strongly heterogeneous. Network topology determines both the convergence rate to normality and whether the limiting distribution is Gaussian. In dense networks whose degree heterogeneity does not vanish, we further show that assortativity can fail to be a valid test statistic even though Moran's $I$ remains well behaved, whereas a dominating node invalidates both.

Spectral Recovery of Point Clouds from Noisy Geometric Graphs

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.08634v1 Announce Type: new Abstract: We study the problem of recovering low-dimensional latent geometry from a random geometric graph generated by noisy, high-dimensional data. Specifically, we analyze the performance of a spectral embedding algorithm on the Signal+Noise Graph Model, in which vertices are associated to points perturbed by Gaussian noise, and edges are included for pairs whose inner product exceeds a specified alignment threshold. In the high-dimensional regime where the number $n$ of points and the ambient dimension $d$ both tend to infinity, we show that under a spectral gap condition, the top eigenvectors and eigenvalues of the graph's adjacency matrix can be used to approximately recover the point cloud up to an orthogonal transformation. We illustrate our results on point clouds sampled from nested spheres and high-dimensional sinusoid curves.

Exact Calibration and Sharp Risk Geometry for Volume-Sampled Ridge Regression

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07721v1 Announce Type: new Abstract: We study ridge regression from exactly $s$ distinct rows of a fixed design. Responses are fixed, and only the subset is random. The determinant law and selected ridge fit share one positive definite penalty. Established mean identities and exponential-family duality give the unique penalty that matches a prescribed full-data ridge fit in expectation. It exists exactly when $s$ exceeds the target's effective dimension. Our main result concerns centered covariance risk normalized by full-data penalized loss. For balanced signed coordinate replicas, a strict sector inequality gives the sharp risk and all maximizing responses at every budget from the dimension to one below the row count. This holds for any nonzero positive semidefinite query. With the target and query fixed, the maximizing response space is unchanged across these budgets. For general designs, we characterize attainment of a leave-one-out envelope. For existing real equiangular tight frames, flat row query energy characterizes when every nonzero residual response maximizes at two deletions. At three deletions, we give the sharp risk and complete maximizing space for isotropic queries, using unequal triangle weights. The balanced geometry yields a same-sample unbiased ridge--Horvitz--Thompson mixture with lower sharp risk and an exact mean-share improvement boundary. Under full recalibration after feature changes, we prove quadratic regret from searching the complete old maximizing space and a query-uniform bound on the mixture's risk gain. The strongest sector inequalities have exact computer-assisted proofs.

Convex Order Beyond Dimension One: Projection Tests, Counterexamples and Gaussian Mixtures

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07404v1 Announce Type: new Abstract: In actuarial science and quantitative finance, convex order provides a natural way to compare risks with the same mean. In dimension one, convex order is well understood through several characterisations. In higher dimensions, a natural approach is to compare all one-dimensional projections, but, although necessary, the resulting condition is in general not sufficient for multivariate convex order. A simple counterexample due to Pinelis exploits Popoviciu's inequality. We revisit this example using gauge functions, and show that gauge functions themselves do not suffice to characterise multivariate convex order for symmetric distributions, even in dimension two. We then show that the radial case makes the source of the failure transparent and construct radial counterexamples in every dimension at least two. Nevertheless, projection tests are sufficient for some important families of distributions. In particular, this is the case for linear transformations of a common radially distributed random vector. This framework includes elliptical distributions generated from a common radial distribution and, in particular, centred Gaussian distributions. Beyond comparisons between Gaussian distributions, Jourdain and Pag\`es recently studied the comparison of a Gaussian distribution with a Gaussian mixture, obtaining necessary conditions and sufficient conditions whose equivalence was left open in general. In this paper, we settle the comparison of a centred Gaussian distribution with a mixture of two centred Gaussian distributions: in every finite dimension, the Gaussian is dominated by the mixture in multivariate convex order if and only if all one-dimensional projections are ordered in convex order.

Minimax Operator Learning for Holomorphic Maps between Hilbert Spaces

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07295v1 Announce Type: new Abstract: We consider the problem of learning nonlinear operators $G_0: \mathcal X\to \mathcal Y$ from finitely many noisy observations. While finite-regularity classes such as Lipschitz- or $C^k$-operators suffer from the curse of sample complexity (i.e. algebraic sample complexity is impossible), algebraic convergence rates can be obtained for holomorphic operators. In this paper we study information-theoretic minimax rates for estimating holomorphic operators. We provide algebraic upper and lower bounds of the metric entropy of holomorphy classes (matching up to an arbitrarily small loss in the exponent) as well as statistical minimax lower bounds in both the random-design and a Gaussian white noise model. For the mean squared error, our novel lower bounds match our upper bounds (up to an arbitrarily small loss in the exponent) and coincide with the convergence rates obtained previously for related holomorphy classes (arXiv:2412.17582). Finally, we apply the theory to the parameter-to-solution map and the parameter-to-quantity-of-interest map arising from the elliptic Darcy flow equation.

Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.07240v1 Announce Type: new Abstract: Let $\theta \to \mathcal G(\theta)$ be a map from a parameter to the solution of some non-linear partial differential equation modelling a dynamical system. We provide conditions to show posterior consistency for $\theta$ under observations of $\mathcal G(\theta)$ with dependent noise, modelling potential time-correlations of the sensors used to make the measurements. We provide two examples, namely the Navier-Stokes equations with unknown viscosity and initial condition, as well as a Reaction-Diffusion type equation with diffusivity coefficient that is varying (heterogeneous) in space, which requires novel stability estimates for a Darcy transport operator with accumulation in time.

History-Conditioned Inference of Memory and Stochastic Forcing in Generalized Langevin Equations under L\'evy Noise

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.06879v1 Announce Type: new Abstract: We consider the identification of memory and stochastic forcing in a one-dimensional generalized Langevin equation with state-dependent Brownian noise and optional additive symmetric $\alpha$-stable jumps. A finite-dimensional Markov embedding provides Kramers--Moyal conditional moment relations that separate memory drift, Brownian diffusion, and jump contributions. From increment ensembles conditioned on the observed velocity history, truncated statistics estimate the stable parameters, corrected second moments determine the Brownian amplitude, and first moments lead to a Volterra equation for the memory kernel, solved by RKHS regularization. We establish conditional finite-sample bounds for the moment estimators and a conditional $L^2$ error bound for kernel recovery with a data-selected regularization parameter. Numerical experiments examine Brownian and Brownian--L\'evy models under different forces, memory kernels, observation lengths, measurement noise, and approximate history conditioning.

Optimal Linear Functional Estimation for Proportionally High-Dimensional Linear Models

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.06875v1 Announce Type: new Abstract: We study estimation of a linear functional in random-design linear models when $\gamma=p/n \in (1, \infty)$ under the dense regime where the design covariance is unknown, and neither the regression vector nor the precision matrix is assumed sparse. Suppose the spectrum of the design covariance belongs to $[\ell,L]$, we establish the minimax mean squared rate for the linear functional has the order $n^{-\alpha(\kappa,\gamma)}$, where the exponent $\alpha(\kappa,\gamma)$ has an explicit elliptic-integral representation and $\alpha(\kappa,\gamma) 1$ and $\gamma > 1$. We propose the Bocca estimator, which combines empirically calibrated resolvents through a complex contour integral to attain the optimal rate.

Entropy-Based Goodness-of-Fit Tests for Generalized $\kappa$ -Gaussian Distributions

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2610.06873v1 Announce Type: new Abstract: We introduce this class of multivariate Kappa-Gaussian distributions by maximizing a type of Kaniadakis $\kappa$ entropy subject to certain first- and second-moment constraints. This differs slightly from the approach of R\'enyi and Tsallis, because the $\kappa$-entropy arises from a relativity-consistent deformation of the exponential and logarithmic functions and yields a family of distributions whose tails follow a power law, a family that actually reverts to the standard Gaussian distribution as $\kappa \to 0$. We then create a $k$-nearest-neighbor (NN) estimator for $\kappa$-entropy and describe it using the difference between two NN functionals involving sums of powers. Next, we establish $L^2$-consistency and asymptotic normality, using the well-known subadditive Euclidean functional and moment expansion framework for NN entropy estimators. Furthermore, using a scaling identity for the $\kappa$-exponential, we derive a closed-form formula for the entropy of the $\kappa$-Gaussian distribution itself. From this, we determine the exact threshold value $\kappa 2$'' condition in the Student's-$t$ distribution. With these components, we construct a non-parametric goodness-of-fit test and then verify it through simulations. Finally, we mention the Sharma--Mittal entropy, which combines the R\'enyi and Tsallis entropies as a natural direction for future work.

A computationally-tractable measure of global sensitivity for sampling-based Bayesian inference

Wed, 07 Oct 2026 00:00:00 -0400

arXiv:2605.28099v4 Announce Type: replace-cross Abstract: Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice. Unfortunately, existing sensitivity methods are rarely applicable in modern Bayesian workflows due to their high computational cost and poor performance in moderate to high dimensions. To address these limitations, we introduce a new approach to global sensitivity analysis based on the Fisher divergence. Our method only requires a set of samples from a reference posterior and the ability to evaluate score functions, making it broadly computationally tractable. Under mild regularity conditions, it controls changes in the whole posterior, and provides a bound on the impact of perturbations on the first two moments. We demonstrate these strengths on challenging Bayesian inference problems which are practically out of reach of existing approaches, including generalised Bayesian inference for unnormalised models, inference in Bayesian models of time series, and neural simulation-based inference.

Reconstruction-Aware Distribution Matching for Inverse Problems with Unpaired Data

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06297v1 Announce Type: new Abstract: Recovering the forward operator of an imaging system from unpaired data avoids both calibration hardware and the clean/degraded pairs that supervision requires-pairs that, for a real lens, are often impossible to acquire. Existing unpaired approaches that explicitly estimate the forward operator by distribution matching evaluate a candidate only through the measurements it generates, whose distribution should match that of the real ones. Components suppressed by the operator are barely present in the degraded images, and therefore barely constrain the operator under such a criterion. Yet inversion precisely tries to recover them. As a result, two operators that are nearly indistinguishable as forward models can invert very differently. We address this by adding a comparison on the clean side: real degraded images, once restored, should be distributed like clean ones. Restorations are computed by a differentiable plug-and-play algorithm parameterized by the operator being learned. On spatially varying PSF calibration and blind super-resolution, the method recovers more accurate operators than degraded-side matching alone, and closes much of the gap to restoration with the true operator.

Finite-Sample Distribution Theory and Efficient Large-Scale Inference for Online Quantile Regression

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05869v1 Announce Type: new Abstract: This paper studies online quantile regression for large-scale and streaming data using Stochastic SubGradient Descent (SSGD) with constant learning rates. Classical offline inference for quantile regression is computationally and memory intensive. Existing works of online inference for quantile regression provide only asymptotic guarantees and typically require sub-exponential tail conditions for distribution theory. To bridge these gaps, we introduce new techniques to prove a quenched central limit theorem (CLT) and finite-sample Gaussian approximation for SSGD under a finite-moment assumption. We further show that Ruppert-Polyak averaging with a constant learning rate has a non-vanishing bias and fails to satisfy CLT centering at the population target. Hence we propose suffix averaging to address this issue and establish its finite-sample Gaussian approximation. Based on these results, we provide an efficient online inference method for quantile regression that avoids covariance estimation. Numerical experiments show that our method achieves desirable empirical coverage rates and competitive performance compared to other inference methods. We also apply our approach to U.S. wage data to demonstrate its practical effectiveness.

On the Sequentially Semiseparable Structure of SDE-Induced Kernels and Efficient Algorithms for Kernel-Based Estimation Problems

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05856v1 Announce Type: new Abstract: We study kernel functions induced by a linear time-invariant (LTI) stochastic differential equation (SDE), an approach that embeds prior knowledge about the function to be estimated directly into the state-space description of the SDE. This kernel-design perspective is relevant across the many settings where kernels play a central role, including kernel methods in statistics, Gaussian process (GP) regression in machine learning, and kernel-based regularization methods in system identification. The resulting class of SDE-induced kernels includes several kernels of practical interest, such as Mat\'ern kernels with half-integer smoothness, spline kernels, and related kernels used in system identification. In contrast to existing linear-time GP regression methods for these kernels, which are typically based on Kalman filtering and Rauch--Tung--Striebel smoothing on the latent state, we work directly with the SSS representation of the observed covariance matrix. This yields linear-complexity recursive algorithms for the matrix operations required in GP regression, including factorization, linear solves, log determinants, posterior covariance, log-marginal-likelihood gradients, and posterior sampling; the same generator-level recursions extend, with only minor modifications, to the analogous computations in kernel-based regularization methods for system identification. Compared with previous uses of SSS representations in GP regression, we derive efficient recursive algorithms for analytic marginal-likelihood gradients in three application-relevant cases, and we develop new recursions for posterior computations and Matheron-type sampling. Numerical experiments verify the accuracy of the proposed recursions and illustrate posterior inference and sampling for representative SDE-induced kernels.

Isotropic Gaussian Processes Improve Vanilla Bayesian Optimization in High Dimensions

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05780v1 Announce Type: new Abstract: High-dimensional Bayesian optimization (BO) often fits Gaussian process (GP) surrogates from far fewer observations than input dimensions. Modern Vanilla BO can perform well in this regime with dimension-aware priors, initialization, and acquisition optimization, but it typically retains automatic relevance determination (ARD), fitting one lengthscale per input coordinate. We study this modeling choice and propose Iso-BO, a controlled modification that replaces the ARD GP with an isotropic GP using one shared lengthscale while keeping the surrounding BO pipeline matched. For radial kernels, we show that the marginal log likelihood (MLL) depends on the inverse-squared ARD lengthscales only through weighted pairwise distances among the observed inputs. The current design can therefore leave some ARD directions exactly invisible or only weakly constrained by the MLL. Iso-BO removes coordinatewise reweighting and fits a single shared scale instead. Lengthscale-fitting and predictive-density diagnostics show that this finite-data effect appears in practice, including when the data-generating process is anisotropic. Across GP-prior, synthetic, and real-world benchmarks, Iso-BO often improves over matched modern Vanilla BO and remains competitive with the included high-dimensional BO baselines under the tested budgets. Stress tests also show the expected boundary wherein sufficiently strong, learnable anisotropy can favor the more flexible ARD model.

Retrieval-Based In-Context Learning: A Domain Adaptation Framework

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05717v1 Announce Type: new Abstract: In-context retrieval (ICR) is a retrieval-based form of in-context learning (ICL) in which demonstrations are retrieved from a source database based on similarity to the query, rather than sampled independently. In this work, we formulate ICR as a type of domain adaptation problem, where the source distribution $P$ of the database may differ from the target distribution $Q$ of the test query-label pair. We investigate the performance of ICR under a flexible class of distributional shifts that substantially extends prior work \citep{li2024fine,guo2025retrieval}, and establish theoretical guarantees that quantify the benefits and pitfalls of this learning paradigm. Our theory is verified by experiments on synthetic and language tasks.

Two-Sample Testing via Path-based Inference

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05684v1 Announce Type: new Abstract: Modern deep generative models are primarily studied for their ability to generate realistic samples, yet the generative dynamics they learn can also serve as objects of statistical inference. We develop this idea for two-sample testing, the problem of deciding whether the same distribution generated two finite datasets. Using stochastic interpolants, we connect both distributions to a shared Gaussian bottleneck, so that each half of the resulting path is a Gaussian channel acting on a single population. We prove that the null hypothesis holds if and only if the population denoiser, or equivalently, the velocity fields of the two halves, coincide at any single noise level, which amounts to a reflection symmetry of the path about the bottleneck. Deviations from this symmetry yield a continuum of two-sample witnesses, which we estimate via held-out regression risks on learned denoisers and velocities and aggregate along the path; under an information-theoretic weighting, the aggregated discrepancy equals the Jeffreys divergence between the noise-smoothed distributions. Calibrating the resulting statistics by permutation yields tests that are valid in finite samples for any trained networks and consistent when the fields are learned accurately. On a synthetic benchmark and three image benchmarks, the proposed tests improve power over the strongest baseline by up to 33 percentage points at an equal total sample budget, with the best choice of regression representation and path weighting depending on the data modality. These results show that generative paths provide a principled representation for statistical testing, extending stochastic-interpolant models beyond generation.

Gaussian Limits for SGD Without Stationary Moments

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05599v1 Announce Type: new Abstract: Temporal dependence can separate the Gaussian approximation of stochastic gradient descent from its stationary moments. For unmodified least-squares SGD, we construct a design with standard Gaussian marginals whose stationary error has every positive moment infinite. Independent observations with the same marginals instead give finite stationary variance. Both regimes retain a Gaussian small-step limit. Our general theory establishes pathwise contraction from a finite second design moment, then uses score cancellation and localization to obtain stationary Gaussian and Ornstein--Uhlenbeck limits. Independent Gaussian regression errors yield an exact conditional Gaussian law and total-variation convergence under the same design integrability. Stronger design conditions identify a positive first-order total-variation constant and a deterministic covariance correction with $o(a)$ error. A scalar coverage expansion translates this correction into its inference consequence. Experiments examine distributional error, coverage, and calibration with dependent scores. Together, these results establish precise probability-law approximation beyond moment-based stationary analysis.

Moment-Accurate Gaussian Mixtures for Constant-Step Stochastic Approximation

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05595v1 Announce Type: new Abstract: Local Gaussian models of constant-step learning predict output variability and expected losses, but weak convergence alone does not justify these moment predictions. We establish moment-accurate Gaussian mixtures by matching stationary energy with local Ornstein--Uhlenbeck limits, ruling out quadratic tail mass invisible to weak convergence. For step size $a$, the second-order Wasserstein error is $o(\sqrt a)$, uniformly over invariant laws, using each law's actual root weights. The assumptions combine confinement, descent, finitely many hyperbolic equilibria and root continuity with finite-variance innovations. The result yields observable covariances, expected objective gaps and first-order mean shifts, while allowing singular covariances, compatible saddles and weights without a limit. For additive noise given by a fixed invertible transform of independent standardized Student $t_3$ coordinates, symmetry gives an order-sharp $\sqrt a$ smooth-test bound. Numerical transport calculations demonstrate the value of root-specific covariances; controlled SGD studies assess observable predictions across step sizes, batch sizes and model geometries.

G-CARB: Graph-Localized Conformal Agent Risk Budget for Compositional Harm

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05563v1 Announce Type: new Abstract: Small language model (SLM) agents need safety controls that track consequences across tool calls with little monitoring overhead. A private read, for example, becomes a leak when a later action sends that data outside the system. We introduce CARB (Conformal Agent Risk Budget), which calibrates when to stop an agent using a ledger of harm incurred before stopping. Under exchangeable episodes, standard conformal risk control bounds this declared loss in expectation over calibration and a future episode. G-CARB selects scorer evidence along observable dependencies from private sources to outgoing actions. The ledger still covers the entire executed history, and computing the gate score requires no additional language-model inference. On AgentDojo replay with two 14B backbones, G-CARB roughly halves scorer-input records at intermediate risk budgets while improving autonomous task completion relative to full-prefix scoring; random context of the same size achieves similar gains. Controlled examples show how retaining the relevant dependency can further avoid stopping benign work.

Taylor Representations for Model-Free RL in Networked MDPs

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05456v1 Announce Type: new Abstract: In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate $Q$-functions, but a naive order-$n$ expansion over $N$ agents requires $\Theta(N^n)$ coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.

Variance-Aware Fine-Grained Gap-Dependent Bounds for Online Reinforcement Learning

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04752v1 Announce Type: new Abstract: We study model-free online reinforcement learning (RL) for episodic tabular Markov decision processes, focusing on both gap-dependent regret and policy switching cost. While fine-grained gap-dependent analysis has been established for model-free RL algorithms using Hoeffding-type exploration bonuses, such results for model-free algorithms with variance-based exploration bonuses remain unknown, despite their superior worst-case and coarse-grained gap-dependent guarantees. In this paper, we resolve this open problem by establishing the first fine-grained gap-dependent regret upper bound for UCB-Bernstein+, a refined UCB-Bernstein algorithm, in variance-aware model-free online RL. Moreover, by integrating a stage-wise policy update design into our fine-grained framework and using refined variance-based bonuses, we achieve the best-known gap-dependent local switching cost to date. In addition, our analysis yields improved worst-case guarantees for both regret and local switching cost over the original UCB-Bernstein algorithm. Numerical experiments further demonstrate that UCB-Bernstein+ achieves favorable empirical performance in both regret and local switching cost.

Exact Fast Batch Simulation for Tabular Reinforcement Learning

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04746v1 Announce Type: new Abstract: Simulation is a fundamental computational primitive in reinforcement learning (RL), yet conventional simulation explicitly generates individual trajectories even when downstream procedures use only aggregate statistics. To address this, we develop an exact fast-simulation framework for finite-horizon tabular Markov decision processes. Our framework has two complementary modes. In direct batch simulation, a batch is represented by its aggregate Markov flow. With sufficient parallel simulation resources, this flow can be obtained by trajectory aggregation; when such simulation is unavailable or costly but the initial state and transition distributions are directly accessible, we instead generate an identically distributed flow through forward Markov-flow sampling without materializing individual trajectories. The latter reduces the simulator-side computational dependence on batch size $m$ from $O(m)$ to $O(1)$. In adaptive batch simulation, when batch length is determined by a data-dependent condition, exact multivariate-hypergeometric splitting recursively refines a candidate Markov flow while preserving the conditional law, reducing the cost dependence on $m$ from $O(m)$ to $O(\log m)$. Together, these modes accelerate simulation by keeping trajectories aggregated whenever possible and refining flows only when required to locate data-dependent boundaries. The framework applies broadly across simulator-based, offline, and online batch or stage-based RL, as illustrated with representative algorithms from each setting.

Hypergraph Representation Learning with Hyperlink Random Effects

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04640v1 Announce Type: new Abstract: Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04390v1 Announce Type: new Abstract: Simulation-free training of latent Stochastic Differential Equations (SDEs) relies on a variational posterior process whose one-time marginals are tractable, typically Gaussian. Such marginals, however, do not determine the underlying dynamics: many processes share the same marginals while differing in their temporal structure, and existing parameterizations fix this structure implicitly, which restricts the posterior family and biases the learned model. We introduce Gaussian flow dynamics, which construct stochastic processes directly from smoothly evolving Gaussian marginals while making the marginal-preserving, or gauge, degrees of freedom explicit and parameterizable. The construction admits state-dependent diffusion coefficients and recovers every linear SDE with additive noise and a non-degenerate Gaussian initial distribution. Building on it, we propose Gauge Matching, a simulation-free method for latent SDE learning that combines Gaussian flow dynamics with the SDE Matching objective. Gauge Matching costs at most quadratically in the latent dimension per step, like SDE Matching, but learns the temporal structure of the posterior beyond its one-time marginals. It comes within a nat of Helmholtz-SDE, which computes the gauge from the prior Jacobian at cubic cost, on the linear benchmark where the exact posterior is known, matches it on nonlinear systems, and applies where Helmholtz-SDE does not, to state-dependent noise.

Local Fisher Information Enables Sparse Causal Discovery

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04291v1 Announce Type: new Abstract: Sparse causal discovery calls for methods that exploit graph structure without estimating high-dimensional densities. We introduce Fisher Information Completion Search (FiCS), a source-first algorithm for additive noise models that uses one local Fisher score for both ordering and parent selection. Under regularity and nonconstant-parent conditions, we prove that a node's local Fisher information equals the noise Fisher information exactly when the conditioning set contains all parents, provided that it contains no descendants. This Fisher parent completion identifies the parent set as the unique minimal Fisher completion. With a maximum conditioning set size $q$ at least the maximum indegree $d$, population FiCS queries marginals of at most $q+1$ variables and recovers the true directed acyclic graph under a positive ordering margin. Bounded conditioning also has a population advantage: reducing $q$ toward $d$ cannot decrease, and can strictly increase, the ordering margin. A growing non-Gaussian family separates local Fisher selection from conditional-variance and leaf-first Fisher ordering. For the regularized kernel Stein estimator, we establish high-dimensional DAG consistency under $q\{1+\log(p/q)\}+\log p=o(n)$, uniform Fisher separation, local approximation, and compatible ridge and parent penalty parameters. Experiments show the strongest gains when $n$ is small relative to $p$, quantify the effect of the conditioning size, and demonstrate competitive reference-graph recovery on three real-data benchmarks.

Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04171v1 Announce Type: new Abstract: Inference-time steering combines pretrained diffusion experts or rewards without retraining by changing the dynamics that transport noise to data. Feynman-Kac correction compensates for proposal mismatch through importance-weighted sequential Monte Carlo (SMC), whose finite-particle behavior depends on the proposal. Variance-controlling guidance (VCG) improves that proposal by fitting a linear drift correction to minimize empirical log-weight-rate variance. Although its population optimum cannot worsen residual variance, finite-particle VCG can nearly eliminate its fitting residual while increasing residual risk on new states by orders of magnitude. The resulting update can degrade unweighted generation or accelerate particle collapse. We show that the centered Feynman-Kac rate is the normalized transport residual and that expected out-of-fit benefit is exactly population headroom minus coefficient-estimation penalty. Under regularity assumptions, a Wasserstein analysis bounds the unweighted proposal's terminal error using this residual. These results motivate Risk-Calibrated Proposal Transport (RCPT), which uses deletion leave-one-out residuals to calibrate the retained fraction of the VCG update, adding no model calls and only small linear-algebra overhead. Experiments on 2D checker distributions, scaffold decoration, molecular property optimization, and class-conditional CIFAR-10 generation demonstrate recovery from harmful fitted updates. Across molecular and image domains, RCPT mitigates harmful fitted updates and improves a broad range of terminal metrics relative to uncalibrated VCG.

Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04157v1 Announce Type: new Abstract: Graph Neural Networks (GNNs) often struggle to capture long-range dependencies due to over-squashing -- a phenomenon in which the repeated compression of node embeddings into finite-size messages causes representations to collapse. Over-squashing is most often diagnosed as a property of the graph topology, with effective resistance serving as a principled measure of the bottleneck. We provide a complementary view on the matter: building on cellular sheaves, we introduce sheaf effective resistance, a generalization of effective resistance that depends on the sheaf attached to the graph, and we prove that for flat vector bundles, the over-squashing sensitivity in the Jacobian sense is upper bounded by a quantity related to the sheaf effective resistance between the nodes. The bottleneck thus need not lie in the graph itself: it can be relocated, and reduced, by adjusting the sheaf. We instantiate this idea in FlatNSD, a simple message-passing variant of Neural Sheaf Diffusion, and show that it implicitly learns to modulate total sheaf effective resistance, performing well on benchmarks designed to stress over-squashing without altering the original graph topology.

Adaptive Partitioning Schemes for Optimistic Optimization

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04039v1 Announce Type: new Abstract: Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of "Optimistic Optimization" algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-\beta / d})$ regret, where $\beta = 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. We use our approach to improve the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving $\sim10\%$ improvement in performance relative to the best possible unquantized model.

Probability flow ODEs in score-based and reflected diffusion models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.03846v1 Announce Type: new Abstract: Probability-flow ordinary differential equations (PF-ODEs) are widely used as deterministic samplers for score-based diffusion models. Their usual justification is that the Fokker--Planck equation of a diffusion can be rewritten as a continuity equation driven by the score function of the forward diffusion. This identity does not, however, guarantee that the resulting velocity field generates a well-posed flow. We provide theoretical insights into the design of such deterministic samplers for generative models based on diffusions and reflected diffusions. We identify sufficient conditions for a regular Lagrangian PF-ODE flow to exist; reverse sampling and invertibility require two-sided divergence control. For learned scores, sampler stability is controlled by an unweighted velocity error, exposing a mismatch with density-weighted score matching and motivating architectural control of Jacobians, divergence, growth, and compression. Under the manifold hypothesis, positive-time regularization justifies an early-stopped PF-ODE while constants deteriorate near the data endpoint; an explicit sphere example shows that the exact deterministic flow becomes singular as the noise level vanishes even though the diffusion marginals remain well defined. These theoretical insights translate into concrete design principles for stable, invertible, and constraint-preserving diffusion samplers. We illustrate the practical relevance of these design principles using controlled numerical experiments.

Targeted Active Learning for Preference-Based Treatment Effects on Multivariate Outcomes

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.03824v1 Announce Type: new Abstract: Treatment efficacy is traditionally demonstrated on the basis of a single primary outcome. However, clinical decision-making usually requires consideration of multiple outcomes, balancing expected benefits against potential risks. The relative value assigned to these outcomes varies substantially from one patient to another. Given a preference rule over outcome profiles, treatment effects and optimal policies can be defined and estimated. Such a rule is rarely available in practice: it must itself be estimated from pairwise comparisons of outcome profiles, which are costly to collect from clinical experts. We propose an active learning framework that selects which comparisons to query. Standard criteria maximize the information gained on the preference rule itself. We instead target the quantities of interest, and select the query that most reduces uncertainty on the treatment effect and on the optimal policy induced by the learned rule. Under a Gaussian process model of the preference rule, we derive a closed-form approximation of this criterion. On semi-synthetic data built from a Parkinson's disease cohort with 13 clinical outcomes, our criterion achieves lower treatment effect estimation error and lower policy regret than existing criteria at equal query budget.

A Dirichlet Mixed-Membership Model for Exact Multivariate Distributional Credibility

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05741v1 Announce Type: new Abstract: Credibility theory combines individual experience with portfolio information for insurance pricing, but classical formulations focus primarily on conditional means and expected premiums. We propose a Dirichlet mixed-membership model (DMMM) for multivariate distributional credibility. Policyholder risk is represented by a stable composition over latent risk classes: baseline characteristics determine its a priori assessment, while repeated multivariate experience progressively updates its a posteriori assessment. Support-specific expert distributions accommodate heterogeneous outcomes, with dependence induced through the shared latent structure. The resulting posterior predictive distribution can be written exactly as a convex combination of portfolio and experience components, extending the familiar credibility-factor structure beyond the conditional mean. We study the framework through a simulation experiment and a vehicle telematics application. The simulation shows that relatively simple experts can capture complex multivariate insurance distributions and learn policyholder-specific risk as experience accumulates. In the telematics application, recent claims and driving behaviour provide complementary information for future claim-frequency prediction, allowing similar policyholders to receive different experience-rated assessments. The DMMM therefore provides a flexible and interpretable framework for combining heterogeneous insurance experience while retaining the structure of classical credibility.

Minimax and Adaptive Transfer Learning for Sparse Canonical Correlation Analysis

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05735v1 Announce Type: new Abstract: We develop a transfer learning framework for high-dimensional sparse canonical correlation analysis (CCA) with multiple heterogeneous source datasets. Our goal is to improve estimation of the target canonical coefficient matrices by borrowing information from related sources. We characterize source-target similarity through discrepancies in the joint covariance structure and establish minimax optimal rates under both joint and separate prediction losses, explicitly quantifying the gain from enlarged effective sample size and the cost of heterogeneity. To attain these rates, we first construct an oracle transfer estimator based on debiasing and truncated normalization. We then develop a computationally efficient procedure that adaptively achieves the minimax rate without prior knowledge of the sparsity levels, using aggregation to control transfer bias and a truncated normalization scheme to preserve transfer gains under the scale-sensitive prediction loss. A data-driven source detection procedure is further proposed to identify potentially informative auxiliary datasets. Our analysis also yields a generalized sin-theta perturbation theorem that removes a commonly imposed comparability condition on leading canonical correlations in the sparse CCA problem.

Instrumental Variable Analysis in Underrepresented Subpopulations Powered by Knowledge Transfer

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05680v1 Announce Type: new Abstract: Instrumental variable (IV) analysis in underrepresented target populations suffers from low statistical efficiency and weak IV bias due to limited sample size. Leveraging external knowledge from a source population with larger samples offers an appealing solution to this problem. We propose in this paper the KNowledge-powered IV Estimator for underrepresented Subpopulations (KNIVES), a framework that enhances the IV analysis for underrepresented subpopulations by transferring knowledge from external source population data. KNIVES constructs a knowledge-transferred IV score by combining multiple candidate models through an effective signal-to-noise ratio criterion tailored to the downstream IV estimator, rather than prediction accuracy alone. To address weak associations between the IV score and the exposure, as well as a high correlation among candidate models in the target population, KNIVES employs a bias correction technique to mitigate the resulting bias and ensure robust performance. Theoretical investigation demonstrates that our method is robust to weak IV bias and achieves improved efficiency compared to the causal effect estimator based on any single candidate model. In addition, KNIVES avoids negative transfer by guaranteeing that its asymptotic variance is not larger than that of the estimator relying solely on target population data. Extensive numerical studies demonstrate the superior finite-sample performance of our method over existing methods. Two Mendelian randomization studies on ethnic minority subgroups in UK Biobank data further illustrate the advantages of our method.

Direct Learning of Treatment-Benefit Rankings for Restricted Mean Survival Time in Randomized Trials with Censoring

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05522v1 Announce Type: new Abstract: In precision medicine, treatment decisions often depend more on identifying which patients are most likely to benefit from treatment than on accurately estimating benefit for every patient. However, existing methods estimate patient-specific treatment effects and derive patient rankings as a secondary step. We propose a direct ranking approach for conditional RMST treatment benefit in randomized trials with right-censored outcomes. We first construct a censoring-adjusted orthogonal RMST pseudo-outcome whose conditional expectation equals the true conditional RMST difference. Then, we compare patients pairwise and optimize a smooth ranking loss that directly targets treatment-benefit ordering. The pairwise criterion incorporates orthogonal corrections for estimation of the event and censoring distributions. We show that the population minimizer of the proposed loss induces the same ordering as the true conditional RMST treatment benefit and that the resulting estimating equation is Neyman-orthogonal to nuisance survival and censoring models. In simulation studies with nonlinear treatment-effect heterogeneity and moderate to heavy censoring, the proposed approach improved rank correlation and treatment-benefit enrichment relative to both plug-in RMST estimation and regression of the same RMST pseudo-outcome. Application to a randomized breast cancer trial demonstrated improved identification of patients with greater treatment benefit. In conclusion, the proposed framework combines orthogonal survival learning with pairwise ranking and may be particularly useful in precision medicine settings where treatment prioritization and patient selection are the primary goals.

Variance Estimation Under Local Pivotal Methods

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05464v1 Announce Type: new Abstract: Spatially balanced sampling designs, such as the local pivotal methods (LPM), improve representation of auxiliary-variable space, but design-based variance estimation is challenging because second-order inclusion probabilities are generally intractable and may be zero or near zero. We propose two approaches for estimating the variance of the Horvitz-Thompson mean and the finite-population variance. The first estimates joint inclusion probabilities by Monte Carlo simulation and uses pairwise independence tests to modify the resulting variance estimators. The second, a model-assisted bootstrap (MABS), uses an interpolating Gaussian process to construct a synthetic finite population and estimates variance by resampling under the original LPM design. In simulations, the modified empirical approach performs well when responses are strongly associated with auxiliary variables, but its performance for the Horvitz-Thompson mean deteriorates as this association weakens. MABS exhibits more stable performance across noise levels and sampling settings, including under LPM2 and non-Gaussian noise. For finite-population variance estimation, however, no method shows a uniform advantage. These results illustrate the complementary strengths of the proposed approaches for inference under spatially balanced sampling.

Semi-Supervised Kernel Ridge Fr\'echet Regression

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05388v1 Announce Type: new Abstract: Fr\'echet regression provides a framework for predicting random object-valued responses by minimizing the conditional expected squared distances. We propose semi-supervised kernel ridge Fr\'echet regression (SS-KRFR) to exploit unlabeled covariates when labeled samples are scarce. The method learns kernel spectral features from both labeled and unlabeled covariates, then uses labeled responses to estimate the conditional Fr\'echet function by ridge regression. We derive prediction error bounds that distinguish the roles of labeled and unlabeled samples, and establish polynomial convergence rates under suitable conditions. Under additional kernel assumptions, a sharper analysis relaxes the sample-size requirements for learning the features. We also develop hybrid methods that combine features, predictions, or both from models fitted with and without unlabeled covariates, and establish hybrid stability uniformly over mixing weights in Hadamard spaces at common tuning, with a separate rate guarantee for prediction mixing. Simulations and an EEG application show semi-supervised gain and improvements over competing Fr\'echet regression methods in several settings.

Bayesian Reconciliation of Overlapping Multi-Step Forecasts: A Post-Processing Framework for Cross-Origin Coherence

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05340v1 Announce Type: new Abstract: Multi-step forecasting systems, including modern artificial intelligence (AI) models, often issue overlapping predictions for the same future time from different forecast origins. These predictions can disagree even when produced by the same model, a phenomenon we call cross-origin incoherence. We propose a Bayesian reconciliation framework that treats overlapping forecasts as noisy and potentially biased measurements of a common latent trajectory. The method operates as a model agnostic post-processing layer, requiring no access to the forecasting models architecture, parameters, or training data. A Bayesian state-space model jointly reconciles forecasts targeting the same future time while accounting for horizon-specific bias and uncertainty. Controlled simulations demonstrate substantial reductions in cross-origin incoherence and accurate latent trajectory recovery under the assumed data generating process. An empirical application to daily S and P 500 volatility forecasts reduces 90% prediction interval coverage from 94.8% to 88.3%, closer to nominal coverage, but increases point forecast error. An additional LSTM experiment demonstrates applicability to modern neural forecasting systems.

Same Predictions, Different Harms: Causal Auditing of Patient World Models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05198v1 Announce Type: new Abstract: Patient world models used for clinical trial simulation can agree on transition kernels and arm-specific risks, yet disagree on the fraction of patients harmed by switching treatment---the counterfactual quantity that matters for intervention-aware reasoning. We audit this reliability gap in a two-stage shared-response SCM: a categorical intermediate health state is followed by common terminal care. Under independent stages, the sharp harm interval has closed-form endpoints for at most three intermediate states, with an exactness boundary at four states. Declared dependence and response-mismatch budgets yield calibrated outer bounds when stage independence or complete mediation is relaxed; in a symmetric three-state model the entire sensitivity frontier is sharp, $[0,\min\{1/2,1/3+(\rho+\delta)/2\}]$, and shows exactly how budgets erase the gain over endpoint-only bounds. Two eight-variable response LPs propagate interventional uncertainty for finite-sample audits. Exact witnesses verify attainability. On public clinical simulators (EpiCare; sepsis), native configurations show little resolved stage dependence and no additional joint-compatibility gain over pairwise transport---honest negative results for reliability claims. All experiments are locally reproducible; guarantees remain conditional on the stated causal model. The results provide a concrete protocol for deciding when a patient world model is safe to trust for counterfactual harm.

What does two-sample Mendelian randomization estimate when the exposure-outcome relationship is nonlinear?

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05134v1 Announce Type: new Abstract: Two-sample Mendelian randomization with summary statistics has become a popular MR design in Epidemiology. Its ratio estimate has an average causal effect interpretation only under strong untestable assumptions including linearity. We derive what the per-variant ratio, and the pooled and robust estimators built from it, estimate when a continuous exposure has a nonlinear effect, under two conditions on how genetic variation and unmeasured factors shape exposure: no unmeasured common effect modifier, and an exposure control function. Under either condition, each variant's ratio is a weighted average of the slope of the dose-response curve, with weights that depend on how that variant moves the distribution of exposure and that are nonnegative when the exposure distributions at different genotypes do not cross. Variants that shift everyone's exposure equally target nearly the same quantity; variants acting at particular doses or on the spread of exposure target different ones, some outside the range of any individual effect. Pooled estimates therefore have no fixed interpretation, heterogeneity tests and MR-Egger misread nonlinearity as pleiotropy, and summary statistics cannot reveal the problem, even when the dose-response curve is identifiable from individual-level data. For continuous exposures, two-sample estimates rest on a linearity assumption that should be stated and defended; individual-level exposure data resolve the problem and should be prioritized.

A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04964v1 Announce Type: new Abstract: Finite discrete count data are ubiquitous in fields such as biomedicine and social sciences and these data frequently exhibit over-dispersion, rendering the binomial distribution inadequate for modeling. Although the beta-binomial distribution mitigates this by assigning a subjective beta prior to the success probability, its reliance on a pre-specified parametric shape may result in biased representations of prior information, failing to capture the complex and heterogeneous characteristics of real-world data. To address these limitations, this paper proposes a novel Bernstein-binomial model. By leveraging the uniform approximation properties of Bernstein distribution, we construct a highly flexible and general prior framework for the success probability in binomial distribition, which dynamically adapts to complex data structures, avoiding the subjectivity and restrictions associated with conventional unimodal priors. A comprehensive theoretical framework for both frequentist and Bayesian inferences is established. Furthermore, the model is extended to a regression setting to account for covariate effects. Extensive simulation studies and real-world data applications confirm that the proposed Bernstein-binomial model significantly outperforms existing models. It offers superior fitting accuracy, robustness, and out-of-sample predictive performance when modeling over-dispersed counts with complex latent prior structures.

Noisy Matrix Completion under Informative Missingness

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04859v1 Announce Type: new Abstract: Noisy matrix completion is a fundamental problem in statistical learning and has attracted a substantial amount of interest over the last two decades. In a variety of applications, the missingness pattern is highly informative, yet it has received relatively less attention. Most existing methods either overlook this source of information or oversimplify its generating process, with few attempting to model the association between the data matrix and its informative missingness. In this study, we propose a general modeling framework that jointly models the data matrix and its missingness pattern using a pair of low-rank models coupled by a flexible shared linear structure. This joint low-rank approach incorporates the informative missingness to improve matrix completion and can flexibly capture various associations between the two modes of data. We develop an efficient joint estimation procedure for this framework based on projected gradient descent, and establish local convergence guarantees that unveil its computational and statistical properties. We further demonstrate, through extensive simulation studies and real-world data analysis, that our proposed approach outperforms competing methods, achieving substantial improvements in prediction accuracy on missing entries.

Calibration Assessment for Nested Uncertainty Sets

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04790v1 Announce Type: new Abstract: We present a Bayesian framework for assessing the calibration of nested uncertainty sets from simulation studies. Calibration is typically evaluated by repeatedly simulating data from a known model and comparing empirical coverage probabilities with their nominal values, an approach that often requires hundreds or thousands of independent model evaluations to obtain reliable estimates. Such computational demands can be prohibitive when the forward models are expensive to evaluate, for example in data assimilation using a large Earth-system model, or may not be applicable, for exmaple when the output of the simulation is a single or multiple uncertainty sets rather than a full distribution. We present a method that leverages the nested structure of uncertainty sets across nominal coverage levels to assess the calibration of these models. The method, which is based on a Dirichlet-Multinomial model, allows for testing both exact and region-based notions of model calibration in an efficient manner using Bayes factors. Unlike methods that require a full predictive distribution, this method works for procedures that directly produce prediction or confidence intervals. We demonstrate the method on a data assimilation problem containing model form error and show that it is capable of detecting miscalibration even when there are only a limited number of simulation studies available.

Identifying compromise solutions across multiple treatment benefit-harm profiles in multivariate network meta-analysis

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04711v1 Announce Type: new Abstract: Health technology assessment often aims to balance evidence across multiple treatments and outcomes and assess treatment benefit-harm profiles. Multivariate network meta-analysis (mvNMA) is well suited to this task, as it synthesizes evidence across treatments and outcomes. However, the potential of mvNMA has been overlooked, leading decision-makers to rely on outcome-specific NMAs that ignore outcome correlations. Based on independent NMA models, previous work proposed methods such as multivariate P-scores or spie charts to assess treatment benefit-harm profiles by yielding across-outcomes treatment hierarchies. In this article, we propose an mvNMA-based framework for assessing treatment benefit-harm profiles. Our framework uses a hybrid-correlation mvNMA model and incorporates DuMouchel priors for treatment effects, enabling estimation of all treatment effects even when outcomes are missing for some treatments. We then extend common NMA ranking metrics, including SUCRA, the probability of being best, and median ranks, to the mvNMA setting. Based on these metrics, we adapt the VIKOR algorithm for mvNMA. This deterministic multicriteria decision method quantifies overall and worst-case treatment performance and, by balancing these aspects, produces an across-outcomes ranking while identifying treatments offering the optimal compromise between these two aspects. To facilitate use of our framework, we developed the R package mvnma. We applied our framework to two clinical datasets: one comparing eleven physical therapy treatments across two outcomes and another comparing nine antidepressants across five outcomes. Our framework provides an alternative strategy for assessing treatment benefit-harm profiles across multiple outcomes and encourages multivariate approaches in applied clinical and policy settings.

Estimation and inference in penalized function-on-function regression with dependent residual curves

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04677v1 Announce Type: new Abstract: Penalized function-on-function regression, as implemented in the R package refund, treats all grid values of all curves as independent. Residual curves are smooth, so values within a curve are dependent. We study what this does to point estimates and pointwise confidence intervals, in a simulation with Gaussian, count and binary responses and in a plasmode study built on nine real datasets. Under within-curve dependence, model-based 95% intervals cover 0.63--0.82. A curve-clustered sandwich covariance with a leverage adjustment for the penalized hat matrix (CL2), computed after the usual REML fit, brings coverage close to nominal in the simulation; in the plasmode study it is a few points short on eight datasets and 0.84--0.91 for the coefficient surface on the ninth. Satterthwaite degrees of freedom recover most of the remaining shortfall except on that dataset, also with only 20 curves, at the cost of wider intervals. REML, however, undersmooths the coefficient surface: its error is two to four times that of a fit whose smoothing parameters are chosen by curve-blocked neighbourhood cross-validation (NCV), and its CL2 intervals for the surface are wide. Intervals centred at the smoother NCV estimate are narrow but undercover, the familiar tension between estimation and pointwise inference in nonparametric regression. We recommend the NCV estimate to describe the shape of the surface and REML + CL2 with Satterthwaite degrees of freedom for inference. For a surface that is zero everywhere, under dependent errors, these intervals exclude zero at about 5% of the grid points, and the NCV estimate is five to seven times closer to zero than REML's. For fitted means, intercepts and scalar effects, REML + CL2 intervals are close to nominal, except for binary intercepts and scalar effects and for misregistered counts. We state which defaults of refund the evidence supports.

Personalized Federated Vector Autoregression with Personalization Diversity

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04474v1 Announce Type: new Abstract: Personalized federated learning can improve estimation for high-dimensional time series while preserving client-specific dynamics. However, parameter heterogeneity creates a fundamental ambiguity between shared and personalized structure. We introduce the principle of personalization diversity, under which genuinely personalized effects recur in only a limited fraction of clients. Based on this principle, we propose PerFeCT-VAR, Personalized Federated Vector Autoregression via Frequency-Capped Thresholding, which decomposes each client-specific transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures. A cross-client frequency cap yields a sharp shared--personalized separation threshold and motivates frequency-capped thresholding for federated estimation. Our theory further accounts for heterogeneous client distributions through a distributional compatibility condition and establishes joint linear convergence of the shared and personalized components. Under sufficient personalization diversity, the shared dynamics retain federated total-sample-size gains while the personalized components achieve client-level accuracy. Simulations and an application to multi-store retail revenue data demonstrate the predictive and interpretive benefits of the proposed framework.

Cauchy-Combined Hettmansperger-Randles Location Tests in High Dimensions

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04251v1 Announce Type: new Abstract: High-dimensional mean testing is challenging under strong dependence and heavy tails, since classical Hotelling statistics are ill posed and regularized versions based on sample moments remain sensitive to outliers. This paper develops a robust regularized Hotelling framework for one-sample mean inference under elliptical distributions. The proposed HRST statistic combines a Hettmansperger-Randles spatial location estimator with the inverse of a trace-normalized shrinkage Tyler scatter matrix, and calibrates the resulting quadratic form through ridge-resolvent random-matrix theory rather than sparse covariance or precision-matrix assumptions. In the regime $p/n\to y\in(0,\infty)$, allowing a vanishing lower bulk edge and finite-rank diverging spikes, we establish feasible asymptotic normality for each shrinkage level, derive local-alternative distributions with explicit noncentrality parameters, and prove joint Gaussian limits over finite shrinkage grids. These results justify an adaptive Cauchy combination test across shrinkage levels. Simulations and a paired tumor-normal gene-expression study show that HRST maintains size and improves robustness under heavy-tailed distributions while retaining power under strong correlation.

Neyman-Pearson Classification with Indecisions: Simultaneous Control of Selective Type I and Type II Errors

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04233v1 Announce Type: new Abstract: Binary classification often requires controlling both type I and type II error rates at prespecified levels. When the class distributions overlap substantially, the two error limits may be incompatible if every observation must be classified. We study Neyman-Pearson classification with indecisions (NPI), which permits uncertain observations to remain unclassified and assesses selective type I and type II errors among definitive classifications within each class. For an independently trained score, we develop a model-free calibration procedure that combines all candidate threshold pairs passing calibration into a rule whose decision region contains that of every passing candidate. We couple the entire threshold search to a common martingale within each class and compute its finite-horizon crossing probability exactly, avoiding a multiplicity adjustment for the number of candidate pairs. The resulting classifier satisfies both population selective error limits simultaneously with user-specified high probability in finite samples, without assumptions on the accuracy of the fitted score. We bound the additional indecision due to calibration and evaluate the procedure in simulations and applications to recidivism and credit-default prediction.

Score-based confidence intervals for variance-covariance parameters in linear mixed models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04181v1 Announce Type: new Abstract: We propose confidence intervals with near-nominal coverage of variance-covariance parameters in linear mixed models, even when interest or nuisance parameters are near the boundary, that is, when some random effects have small variances or are strongly correlated. In such settings, our simulations show standard Wald, likelihood ratio, and score intervals with nominal level 95% can have coverage as low as 45% and as high as 99%, while the proposed intervals are near nominal. The proposed intervals invert a modified profile score statistic based on the restricted likelihood, with nuisance parameters estimated on an extended parameter set. In a longitudinal study of socialization in children with autism, where the estimated correlation between the random intercept and slope is near minus one, our intervals show that children who start higher improve more slowly. In a genetic study of white blood cell count in mice, they distinguish the contributions of variant classes even though several intervals include zero. Compared to universal inference intervals, which are valid in finite samples, ours are 1.7 to 3.1 times narrower, and finite where one universal interval is not, at a forty-seventh of the computing time. We establish asymptotically correct coverage uniformly in the parameter under a condition known to hold with independent clusters and crossed random effects.

Consistent Spatial Clustering of Complex Objects via Bregman Geometry

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04166v1 Announce Type: new Abstract: Spatial clustering increasingly involves complex objects, including probability distributions, networks, and structured matrices, for which conventional parametric likelihoods may be difficult to specify. We construct a generalized likelihood by exponentiating a cluster-specific Bregman loss on fixed representations of the responses, avoiding the need to specify a parametric sampling model for each response class. Each cluster is associated with an unknown representative, and the generalized likelihood measures within-cluster homogeneity through the Bregman divergence between the represented observations and that representative. A prior family matched to the Bregman geometry yields conjugate generalized posterior updates and permits exact marginalization of the cluster-specific representatives. The resulting collapsed scores combine within-cluster Bregman dispersion with uncertainty in the representatives, while a spanning-tree partition prior restricts posterior partition support to spatially contiguous clusters. This collapsed representation also leads to a tractable MCMC algorithm for posterior computation. The framework accommodates multiple complex-object response classes within a common inferential construction. We establish posterior consistency for the spatial partition and cluster-specific representatives under infill-domain asymptotics. Simulation studies with different complex-object responses demonstrate accurate recovery of spatial partitions and cluster-specific representatives. We further analyze racial-composition distributions across spatial units in Houston, illustrating geographically coherent clusters with distinct demographic compositions.

Co-Supervised Tree Synthesis for Interpretable Subgroup Identification and Honest Treatment Effect Inference in Randomized Trials

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.03927v1 Announce Type: new Abstract: Identifying patient subgroups with heterogeneous treatment effects is central to precision medicine, yet existing approaches face a tension. Black-box methods estimate individualized effects well but yield no interpretable subgroups, while tree-based methods produce explicit partitions but are unstable and less accurate in moderate-sample trials. We propose CausalSynthTree, a co-supervised method in which black-box causal estimators guide construction of an interpretable tree. It partitions the covariate space into cells, fits cell-wise conditional average treatment effect models from both observed data and synthetic data labeled by black-box causal teachers, and synthesizes them into a tree through a treatment-effect disparity criterion. Each leaf carries a sparse linear model, so the tree path defines a subgroup and the leaf model shows which covariates modify the effect. Honest inference for leaf-wise effects remains valid despite co-supervised augmentation and data-driven subgroup selection. In simulations it closes much of the gap between the two families. From moderate sample sizes onward it is more accurate than the black-box learners whenever the effect is linear or has a single threshold, and trails them only on a finer partition than the tree it grows. It controls spurious splits and attains nominal coverage throughout. In the ACTG175 HIV trial, where standard interaction tests detect no effect modification, the method reports no subgroups while the competing tree methods report several. In an adjuvant colon cancer trial it reports a borderline covariate in part of the resamples, together with a within-region age gradient that is consistent with an independent test.

BFI: An R Package for Bayesian Federated Inference

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2609.27977v2 Announce Type: replace-cross Abstract: Bayesian Federated Inference (BFI) estimates statistical models from multicenter data when individual-level observations cannot be combined across centers. We present \pkg{BFI}, an \proglang{R} package that implements this methodology for Gaussian, binomial logistic, and survival regression models. Each center performs a Bayesian maximum a posteriori analysis and sends only parameter estimates and curvature information to a central server, where these summaries are combined to approximate the analysis of the combined data. The package supports prior specification, structured forms of between-center heterogeneity, several parametric and flexible baseline-hazard models for survival analysis, and treatment-effect estimation for observational and randomized studies. We describe the software design and the information exchanged between centers, give reproducible workflows for these analyses, and compare the federated results with pooled-data analyses for Gaussian, logistic, and survival models.

A space of inference spaces in the space sciences - parametric Bayesian inference in astronomy, cosmology and particle physics

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2608.06078v2 Announce Type: replace-cross Abstract: A sample of parametric Bayesian inference applications from astronomy, cosmology and particle physics is studied, augmented by mock data sets and toy problems. The parameter spaces of these parametric physical models and their posterior distributions from analysing specific data are characterized by (1) the number of model parameters, (2) whether the posterior shape is similar to a Gaussian, (3) whether the posterior has light or heavy tails, (4) how small the posterior is compared to the prior, i.e., how informative the data are, (5) whether some parameters remain unconstrained while others are highly constrained, (6) whether the posterior has multiple, disconnected modes, and (7) whether the inference undergoes phase transitions. These axis define a parameter space of inference problems. We characterize each of the inference problems and observe that inference in astrophysics spans the entire parameter space, from low to high dimensionality, mono- to multi-modal, and a variety of complex distributions that range from uninformative to highly informative. Furthermore, the computational cost of the physical models can range from milliseconds to dozens of seconds. The collated sample of inference problems is proposed as a standard test bed for new samplers. For reproducibility and ease of use, a Docker compute image is provided.

High-dimensional reliability-based design optimization using stochastic emulators

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2604.05759v2 Announce Type: replace Abstract: Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem and remains computationally demanding, especially in high dimensions. This paper proposes a new RBDO framework based on a stochastic simulator viewpoint, in which the deterministic limit-state function and uncertain model inputs are combined into a unified stochastic representation. For a given design, the system response is characterized directly through its conditional output distribution rather than through an explicit limit-state function. Stochastic emulators are constructed in the design space to approximate this conditional distribution, enabling semi-analytical evaluation of failure probabilities or associated quantiles without Monte Carlo simulation. Two approaches are considered: generalized lambda models (GLaM) and stochastic polynomial chaos expansions (SPCE). Both yield deterministic mappings between design variables and reliability constraints, thereby eliminating the classical double-loop structure and enabling standard deterministic optimization. The approach is assessed on benchmark problems ranging from low to very high dimension, including stochastic excitation, and compared with Kriging in the full input space and heteroscedastic Gaussian processes in the design space. The proposed method provides substantial computational gains, particularly for high-dimensional random inputs, while retaining comparable efficiency to Kriging in low dimensions. Unlike heteroscedastic Gaussian processes, GLaM and SPCE also avoid restrictive assumptions on the conditional response distribution.

Two Localization Strategies for Sequential MCMC Data Assimilation with Applications to Nonlinear Non-Gaussian Geophysical Models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2603.05817v2 Announce Type: replace Abstract: We present a localized data assimilation (DA) scheme based on sequential Markov Chain Monte Carlo (SMCMC) \cite{smcmc}, a provably convergent method for filtering high-dimensional, nonlinear, and potentially non-Gaussian state-space models. Unlike particle filters, which are exact for such models, SMCMC does not assign weights to samples, avoiding weight degeneracy in small-ensemble regimes. We design two localization approaches within the SMCMC framework that exploit observation sparsity to reduce effective degrees of freedom. The first variant collects observed blocks into a single reduced domain and runs parallel MCMC chains over this combined region. The second further reduces per-chain state dimension by decomposing the observed region into independent blocks with compact halos, applying Gaspari--Cohn tapering to down-weight distant observations. When the observation model is linear Gaussian, the approximate filtering density reduces to a Gaussian mixture from which independent samples can be drawn exactly; otherwise, we employ an MCMC kernel. We test on high-dimensional ($d \sim 10^4 - 10^5$) state-space models, including a linear Gaussian model and a nonlinear multilayer shallow water equation with linear and nonlinear observation operators. We consider Gaussian and Student-$t$ observation noise, showing that LSMCMC handles heavy-tailed errors that cause ensemble Kalman methods to diverge. Observations include synthetic and real SWOT (NASA) and ocean drifter (NOAA) data. We compare the two variants against each other and the local ensemble transform Kalman filter (LETKF).

Weak Poincar\'{e} inequalities for two-component Deterministic-scan Metropolis-within-Gibbs samplers

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2602.14692v2 Announce Type: replace Abstract: Using the framework of weak Poincar\'{e} inequalities, we analyze the convergence properties of deterministic-scan Metropolis-within-Gibbs samplers, an important class of Markov chain Monte Carlo algorithms. Our analysis applies to nonreversible Markov chains and yields explicit (subgeometric) convergence bounds through novel comparison techniques based on Dirichlet forms. We show that the joint chain inherits the convergence behavior of the marginal chain and conversely. In addition, we establish several fundamental results for weak Poincar\'{e} inequalities for discrete-time Markov chains, such as a tensorization property for independent chains. We apply our theoretical results through applications to algorithms for Bayesian inference for a hierarchical regression model and a diffusion model under discretely-observed data.

BKP: An R Package for Beta Kernel Process Modeling

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2508.10447v4 Announce Type: replace Abstract: Estimating input-dependent probability surfaces from binary, binomial, categorical, or multinomial response data is a common task in statistics and machine learning. Latent Gaussian process classifiers provide flexible nonparametric models for such problems, but posterior inference with discrete responses typically requires approximation or simulation. We discuss an implementation of probability-scale beta and Dirichlet kernel models in the \pkg{BKP} package for \proglang{R}. The package implements the Beta Kernel Process (BKP), which uses kernel-weighted pseudo-count aggregation and beta-binomial conjugacy to obtain closed-form conjugate posterior summaries and posterior predictive distributions for binomial probabilities. It also implements the Dirichlet Kernel Process (DKP) for multi-class responses, together with TwinBKP and TwinDKP, scalable twinning-based global-local approximations for larger datasets. The resulting workflow supports transparent kernel-weighted evidence borrowing, several kernel families, fixed and data-adaptive priors, effective-sample-size calibration, loss-based hyperparameter tuning, and standard S3 methods for fitting, prediction, simulation, visualization, and extraction of posterior summaries. Reproducible examples demonstrate probability-surface estimation, binary and multi-class classification, computational comparison, and real-data applications to \emph{Loa loa} infection prevalence mapping and Mourning Warbler distribution modeling.

Dimension Reduction for the Trivariate Normal Product Distribution: An Efficient Numerical Algorithm via Conditional Expectation

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05738v1 Announce Type: cross Abstract: Statistical inference in sequential mediation models requires evaluating the cumulative distribution function (CDF) of the product of three normal coefficient estimators, an operation that entails integrating over a non-convex region with boundary $xyz=v$. While the Delta method provides an instantaneous first-order approximation, its asymptotic variance collapses whenever two or more path coefficients approach zero, producing severe undercoverage near parameter boundaries. Nonparametric bootstrapping avoids gradient collapse but incurs an $O(B \times N)$ computational cost that becomes burdensome in large-scale simulation studies or iterative power analyses. We propose a model-based dimension-reduction algorithm that integrates out the third variable analytically under the trivariate Gaussian distribution for arbitrary mean vectors and positive-definite covariance matrices. Partitioning the $xy$-plane into quadrants isolates the sign change at the coordinate axes, reducing the problem to an adaptive two-dimensional quadrature whose fixed-grid cost is $O(n^2)$ in place of $O(n^3)$. In simulation benchmarks across six parameter regimes, the algorithm achieves a mean absolute error of $3.1 \times 10^{-5}$ relative to a $10^{8}$-sample Monte Carlo reference, evaluating the distribution in under one second and yielding plug-in quantile confidence intervals whose empirical coverage was near or above nominal.

A Bayesian One-Sample Test for the Mean of Functional Data

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05512v1 Announce Type: cross Abstract: In the context of functional data analysis, we propose a Bayesian test to assess whether the mean function of a Gaussian population is identically zero. By leveraging the structure of the reproducing kernel Hilbert space (RKHS) associated with the covariance function of the underlying process, we approximate the mean by a finite linear combination of kernel sections. This finite-dimensional representation arises from the natural assumption that the mean lies in the corresponding RKHS, enabling a parametric Bayesian approach to hypothesis testing through a spike-and-slab prior on the coefficients. Given the absence of a canonical reference measure on infinite-dimensional spaces, the likelihood is expressed via a Radon-Nikodym derivative between induced Gaussian measures. Since the number of kernel sections is unknown, we employ reversible jump Markov chain Monte Carlo (RJMCMC) to explore the trans-dimensional parameter space and estimate the posterior distribution. From the resulting posterior samples we construct estimators of the posterior probability of the null hypothesis and the Bayes factor, providing quantifiable evidence against the null and supporting informed decisions under uncertainty. Furthermore, to validate this methodology we establish near-optimal posterior contraction rates for the proposed test under mild conditions, demonstrate its empirical performance on simulated data sets, and illustrate its application with real climate data.

Improving score-based sampling via affine post-processing

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04773v1 Announce Type: cross Abstract: Sampling from a probability distribution with access only to its log-density is a foundational problem in statistics, machine learning, and the physical sciences. This problem is studied in the data-free score-based diffusion literature, which samples the target density via estimating scores of densities produced by convolution with Gaussian random variables and implementing a reverse SDE. In this framework, score estimators are constructed via Markov chain Monte Carlo, importance sampling, or rejection sampling. The estimators often operate far beyond the regime where mixing time and error control can be established and have large bias and variance when estimating the underlying score. In our method we propose post-processing: splitting a fixed computation budget across multiple evaluations, querying the estimator at different points, and fitting a single pooled estimate via linear combination to minimize bias and variance at a target location. The final value is an affine map of a vector of multiple score estimates. We show this reduces score estimation error when compared to the computation-matched base estimator queried at a single point. We demonstrate improved sample quality over other score estimation methods matched for computation cost on difficult target densities such as log-concave densities with large condition number, multimodal densities, and high-dimensional densities.

Log predictive density score estimation in the presence of outliers

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04748v1 Announce Type: cross Abstract: The log predictive density score (LPDS) and related estimators of the expected log predictive density (ELPD) have become the de facto standard for Bayesian model comparison. The LPDS is a natural out-of-sample measure of predictive density performance that accounts for parameter uncertainty, is less dependent on the prior than the marginal likelihood, and is easily computed sequentially using standard Monte Carlo from posterior draws. Our article demonstrates, however, that the standard Monte Carlo estimate of the LPDS can be extremely variable and severely biased when the test data has outliers, leading to misleading conclusions and suboptimal model choices. Estimating the LPDS as the difference between the log marginal likelihood of the full dataset and the training data is shown to be a dramatically more efficient approach. This estimator is also shown to be a much more effective fallback for observations that have been flagged as problematic by the widely used PSIS-LOO model comparison framework in Stan.

Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04568v1 Announce Type: cross Abstract: We introduce a sampling approach for energy- and score-based generative models that requires no gradient evaluations of the model. Replacing the drift term that would normally contain the score $\nabla_\mathbf{x} \log p_\theta(\bf{x})$ with a high-frequency dithered cosine of the model's \textit{value}, $\sqrt{\alpha\omega}\,\cos(\omega t + k \log p_\theta(\bf{x}))$, produces, in the high-frequency averaging limit, Langevin Markov chain Monte Carlo for energy-based models and the reverse-time SDE of score-based diffusion. We prove that trajectories of the dithered It\^{o} SDE converge to those of the target SDE, driven by the same Brownian motion, uniformly on compact time intervals in probability, by an averaging argument that extends bounded extremum seeking (ES) to It\^{o} processes, with an explicit $O(\omega^{-1/2})$ mean-square rate under global bounds. The approach is not confined to smooth targets: it extends to $C^{1,1}$ energies with discontinuous curvature (without ellipticity requirement) and to Sobolev energies whose Hessians exist only off measure zero sets; for Lipschitz energies with gradient kinks the averaged limit remains well posed; the Krylov-R\"ockner integrability class is the boundary of provability. The approach provides a hard \textit{a priori} bound on the per-step update rate and applies to explicitly time-varying targets on finite horizons. Gradient-free pixel-space sampling is not competitive with well-tuned backpropagation-based samplers at practical evaluation budgets; the regime where the approach offers an advantage is latent-space sampling when the model is a black box and the target drifts in time. We demonstrate latent-space tracking for time-varying images on CelebA-HQ ($256{\times}256$) from limited 1D projection measurements and latent-space EBM sampling on CIFAR-10.

Fully Homomorphic Encryption for Statistical Modeling

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04163v1 Announce Type: cross Abstract: Fully homomorphic encryption allows arithmetic to be carried out on encrypted values, so that a party performing a computation need not see the data it operates on. This is useful wherever collaborating parties or sites cannot share data records or computed summaries yet need to do a joint analysis. We demonstrate the protocols needed to perform such analyses reproducibly via two packages in R, a platform widely used for applied statistics. The first, openfhe.R, is an interface to the OpenFHE C++ library, which exposes exact integer arithmetic (BFV, BGV), approximate real-valued arithmetic (CKKS), Boolean circuits, and multiparty key generation. The second is homomorpheR, which builds a small set of master/worker primitives for multi-party protocols on top of the first. Together, the two let an ordinary R statistical routine compose with an encrypted-arithmetic layer at the function-value boundary, provided the quantity crossing that boundary decomposes as a sum over sites. Two validation studies are presented: distributed stratified Cox regression, where stats4::mle() converges through an encrypted channel, and federated Cox-lasso via convex optimization using consensus ADMM, where the cross-site update is the only encrypted step. We also discuss federated similarity retrieval and two-party prediction. Throughout, the parties are assumed honest-but-curious, and threshold key generation removes the assumption that any single party holds a usable secret key.

Calculating the Expected Value of Sample Information for Observational Studies affected by Confounding

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06377v1 Announce Type: cross Abstract: Background: The Expected Value of Sample Information (EVSI) quantifies the value of collecting additional evidence to inform a health economic model. Existing EVSI methods typically assume idealized data collection mechanisms, most commonly randomized controlled trials (RCTs). However, in many realistic contexts, additional evidence comes from observational studies, which are subject to confounding or other bias. In this work, we define a methodology to calculate EVSI when additional data are observational and confounded. Methods: First, we define a simulation-based framework in which confounded observational data are generated through Inverse Target Trial Emulation (ITTE), a methodology that generates observational data with controlled levels of confounding starting from initial level data or prior information on population structure. Then, we apply inverse probability weighting (IPW) to obtain an adjusted summary statistic of the data targeting the corresponding randomized estimand. EVSI is finally computed using a regression based approach. Moreover, we propose a computationally efficient method to determine the sample size required to recover the EVSI achievable under an idealized randomized design. Results: We apply the methodology to two health economic models: a Normal Normal conjugate model and a chemotherapy treatment model combining a decision tree and Markov structure. We show that EVSI computed from observational data, even after adjustment, is lower than EVSI based on randomized data. The loss in EVSI increases with the level of induced confounding. Conclusions: This methodology extends EVSI when future evidence is expected to be observational and affected by confounding, enabling value-of-information analysis in more realistic and feasible data collection scenarios. It also provides a principled approach to sample size planning when observational evidence is anticipated.

Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06101v1 Announce Type: cross Abstract: Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.

Comparing two approaches for modelling the loss given default of credit cards: Run-off triangles vs regression

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05926v1 Announce Type: cross Abstract: The use of run-off triangles (ROTs) is a common industry practice in estimating the loss given default (LGD) risk parameter when predicting credit losses in banking. We benchmark this industry practice using credit card data against a more sophisticated (though classical) regression-based approach, which is able to leverage various types of input variables in producing loan-level LGD-estimates. This regression-based approach can demonstrably recover the typical characteristics of the 'U-shaped' empirical LGD-distribution, which the ROT-based approach cannot do. First, we critically review the ROT-based approach and identify multiple demerits using data-driven diagnostics. We then estimate a two-stage regression-based LGD-model and favourably assess the model performance of each component (or 'stage'). Finally, we aggregate the LGD-estimates produced by each approach over time, and compare each time series to the mean empirical loss rate over time. The ROT-based aggregates diverge substantially from the empirical rate over most time periods, whilst the regression-based aggregates follow the empirical trends much closer. These results underscore the greater prediction accuracy of the regression-based LGD-model, relative to the ROT-based one. By implication, the former approach is probably better than the latter ROT-based approach when estimating the LGD under the IFRS 9 accounting framework, which prioritises accuracy.

Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05825v1 Announce Type: cross Abstract: Classification problem in the context of highly imbalanced data is a major challenge in many real-world applications (e.g., FinTech, healthcare, etc.). In these cases, the vast majority of instances belong to a single class and a small fraction represent the minority class (often the most critical class). Recently, diffusion models have emerged as powerful approaches to reduce the degree of ``imbalanced-ness'' in the dataset; they work by generating synthetic data by capturing complex data distributions using iterative transformations. However, standard diffusion models are not inherently suited to highly skewed or heavy-tailed data, due to inbuilt quadratic error loss, which lacks the structural sensitivity to capture rare, extreme values, and minority-class nuances. We propose a novel approach, namely, Quantile-TabDDPM, based on a quantile-regularized denoising objective that combines the standard quadratic error loss with a quantile loss term to explicitly capture rare events while preserving the theoretical grounding of the original denoising objective. We extensively evaluated our approach on a real-world credit card transaction dataset characterized by extreme class imbalance. The results demonstrate that the integration of diffusion-based synthetic data generation with a quantile-regularized denoising objective provides a robust and effective framework for fraud detection in highly imbalanced datasets.

Errors of LLM-Assisted Literature Retrieval in Environmental Science: A Comparison Study of Abstract versus Full-text Based Prompts

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05690v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used for literature search and synthesis. However, it is unclear whether they retrieve accurate bibliographic information in environmental science. Therefore, we quantitatively compared the errors of widely used LLM platforms in retrieving references related to original articles from five leading environmental science journals (Energy and Environmental Science, Nature Sustainability, Nature Climate Change, Lancet Planetary Health, and Environmental Science and Technology) published in 2024 to 2025. Claude, ChatGPT, Grok, DeepSeek, Perplexity, and Gemini were used as the LLM platforms. LLMs retrieved 10 references for each of the 50 randomly selected original article using either the article's abstract or its full-text as prompt. The retrieved references were subject to a multimetric score ratio combining validity of bibliographic data, Google Scholar link, digital object identifier, Scopus Electronic Identifier and relevance score (cited by or being the index paper), and the proportion of complete fabrication that failed all metrics. Abstract-only prompt yielded significantly higher accuracy than full-text one. This advantage was confirmed in multilevel mixed-effect multivariable regression after adjusting for journal, platform, and output order. Source journal and the position of a reference within the output list were also independently associated with retrieval accuracy, with lower-listed references associated with lower accuracy. These findings suggest that LLM assisted literature retrieval in environmental science remains moderately accurate and overall inconsistent, varying significantly by platform, journal, prompt type, and output position. Abstract-based prompting, as task-aligned information compression, may outperform full-text one in literature retrieval. Caution should be used when generalizing our findings.

PKComb-BOIN12: A Pharmacokinetically Guided Bayesian Design for Dose Optimisation in Oncology Drug-Combination Trials

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05477v1 Announce Type: cross Abstract: Dose optimisation of two-agent combinations in early-phase oncology trials must jointly balance toxicity, efficacy, and pharmacologically meaningful drug exposure, yet existing model-assisted combination designs use only binary toxicity--efficacy outcomes and leave pharmacokinetic (PK) data unused for dosing decisions. We propose PKComb-BOIN12, a utility-based Bayesian optimal interval design embedding a continuous PK exposure metric into two-agent dose optimisation via a PK-guided escalation rule and a PK-sufficiency constraint on the final admissible set. Two contributions distinguish this design from a direct combination extension of existing single-agent PK-informed designs. First, PK-based elimination uses a coordinatewise order-ideal (down-set) removal rule, so that eliminating a combination for insufficient exposure is licensed exactly by the assumed monotonicity of exposure in each agent's dose, rather than an unjustified scalar summary of combined dose intensity. Second, the pre-specified target exposure is treated as transportable-but-verifiable: a hierarchical calibration mechanism updates the assumed monotherapy-derived target using accruing combination-arm PK data, with a formal bound on the resulting selection bias under transportability violations. A time-to-event extension, TITE-PKComb-BOIN12, accommodates late-onset outcomes. A factorial simulation study spanning realistic scenarios, including one calibrated to a published combination trial, decomposes the source of PKComb-BOIN12's gains over its non-PK predecessor and evaluates robustness to non-monotone exposure, PK-variance misspecification, and target-transportability violations. An R Shiny application supports design evaluation and real-time conduct.

Stance Drift: How AI-mediated Communication Distorts Our Message

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04620v1 Announce Type: cross Abstract: Large language models (LLMs) increasingly mediate human communication, from drafting emails to summarizing scientific reports, yet whether they faithfully preserve a speaker's position remains largely untested. We model AI-mediated communication as a two-step generation-extraction pipeline: one LLM produces an argument from a specified stance, and a second LLM extracts the stance from that argument. We represent the pipeline as a probabilistic state transition over five Likert-type stance categories and define the stance preservation rate (SPR) as the average probability that the extracted stance matches the initial stance. Across 112 debate propositions, none of the nine LLMs tested exceeded an SPR of 0.7 under the default configuration. Three drift patterns accounted for most of the drift: polarization, deviation from neutrality, and flipping. Among the mitigation strategies tested, including in-context learning, multiple extraction with shuffled options, assertion, and reflection, only adding medium reasoning effort to a reflection prompt for GPT-5.4 substantially improved the SPR, to 0.775, yet polarization remained the largest pattern, with 0.119 of the transition mass. An exploratory comparison with human extraction on a single proposition suggests that drift arises at both the generation and the extraction stage. These results point to a fidelity gap in AI-mediated communication, with implications for journalism, policy deliberation, scientific communication, and other domains where opinion-laden messages pass through language models.

Network-Constrained Matching and Randomization-Based Inference for Causal Effects

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04102v1 Announce Type: cross Abstract: Matching is widely used to mimic randomized experiments by forming matched sets in which treated and control units differ only randomly with respect to observed covariates. However, when the study population consists of interconnected units from a single network or a small number of networks, matching solely on observed covariates may produce matched units that are more closely connected in the network than would occur by chance. This increased network proximity within matched sets can induce spurious associations between treatment and outcome when both variables exhibit similar autocorrelation patterns on the network. To reduce spurious associations while preserving the validity of causal comparisons, we propose a new matching method that matches units with similar covariates subject to additional network-proximity constraints. For post-matching inference, we propose a randomization-based procedure for testing the sharp null hypothesis of no causal effect. The inference uses the asymptotic normal approximation and accommodates statistical dependence among test statistics obtained from each matched set without requiring explicit specifications of their correlation structures. We demonstrate the validity and utility of the proposed methods through simulation studies and apply them to the Framingham Heart Study. The matching method and subsequent inference procedure are implemented in the R package netmatchRI.

Community Detection from Aggregated Relational Data: Identifiability and Spectral Recovery

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.03937v1 Announce Type: cross Abstract: Aggregated relational data replaces a fully observed network with a compressed version, where survey respondents are asked questions such as ``How many of your friends belong to group $G$?''. We consequently only observe a matrix $R = OA$ of the adjacency matrix $A$ with a fixed design $O$. In this paper we understand the effects of this compression on community detection under degree-corrected stochastic block models. First, we give guarantees for when it is possible to recover the full network parameters, and then only just the communities under conditions on a diagonal corrected version of $\mathbb{E}[R]$, which can be used to inform experimental design. Secondly, we show that spectral clustering with single linkage exactly recovers communities when $n\rho_n\gtrsim K^2+K\log n$ when there are $K$ balanced communities under ``uniformly spread'' or near-orthogonal designs, and characterize more generally how the design influences rates of convergence. We also introduce second-order ``friends-of-friends'' queries and develop the corresponding theory.

Scale or speed? When do path signatures improve volatility-regime forecasts?

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06690v1 Announce Type: new Abstract: We study when path signatures, increasingly used as model-free features of return paths, improve out-of-sample forecasts of volatility regimes. In daily United States and developed-market equity returns from 2005 to 2025, machine-learning classifiers do not beat a heterogeneous autoregressive (HAR) regression of realized volatility, although signatures improve the classifiers' accuracy and probability forecasts in the United States. Adding raw signatures to the HAR regression itself improves United States forecasts of next-month volatility terciles, raising balanced accuracy by 2.7 percentage points and lowering the ranked probability score after multiple-testing correction, whereas adding conventional volatility features does not; outside the United States no gain survives correction. Controlled Heston experiments explain the pattern: signatures add modestly when regimes differ in variance level, which realized volatility already captures, and more when regimes share one stationary variance law but differ in mean-reversion speed. Better regime identification does not, however, deliver earlier regime-change signals, and no accuracy gain translates into a resolved Sharpe-ratio gain in a volatility-managed portfolio. Signatures thus add information about how volatility evolves, which realized-volatility predictors miss.

Spatio-Temporal Stochastic Interventions for Causal Inference in Climate Science

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05827v1 Announce Type: new Abstract: Estimating causal effects in climate science, such as the effect of anthropogenic warming on crop loss, is challenging because of complex spatio-temporal dependence and the high-dimensional nature of the treatment. To address this dependence and the resulting poor overlap between observed and counterfactual scenarios, we develop a spatio-temporal stochastic-intervention framework for estimating causal effects from climate observations. We introduce a regularized estimator of the stochastic-intervention treatment effect that trades a controlled bias for a reduction in the weight variance caused by poor overlap. Simulation studies show that this estimator attains lower mean squared error than alternative weighting estimators and removes the confounding bias of an unadjusted estimator. We apply the framework to estimate the effect of historical warming on vapor-pressure deficit, a driver of crop stress, adjusting for precipitation, which confounds the effect by affecting both temperature and humidity. In GISS-E2-1-G climate-model simulations, the global effect is distinguishable from zero in every year from 1995 onward, and omitting the precipitation adjustment inflates the global estimate by 47%. Adjustment reverses the sign of the estimate over 8% of global cropland (125 million hectares), where an unadjusted analysis could misdirect adaptation between heat-focused and moisture-focused measures.

Does the AI Productivity Dividend Diminish? Does the AI Productivity Dividend Diminish? A Validated Framework for Identifying the Shape of Firm-Level Returns to Artificial Intelligence

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05629v1 Announce Type: new Abstract: Forecasts of the productivity dividend from artificial intelligence (AI) differ by an order of magnitude, partly because they extrapolate average gains observed among early, highly exposed adopters. Whether those gains scale linearly, flatten, or are competed away is an empirical question about the shape of the return to AI, not its average. This paper develops and validates a design-based framework for measuring that shape with linked firm-worker data. The framework combines a pre-determined, occupation-based measure of firm exposure to generative AI with a continuous-treatment difference-in-differences design around the release of ChatGPT in November 2022, three pre-specified tests of concavity, a decomposition of exposure effects into an adoption margin and a per-adopter return, a doubly robust analysis of use intensity, a staggered-adoption analysis of earlier AI adopters, and a production-function estimator that places AI in the law of motion of productivity. We validate every component on a calibrated synthetic panel of 20,000 enterprises that reproduces the structure of Statistics Canada's linked business microdata and embeds a known concave effect. The estimators recover the true dose-response curve and detect its concavity (slope difference -0.010, standard error 0.003, one-sided p = 0.002); Monte Carlo coverage of the main confidence interval is 0.97, and the concavity test has power of 0.93. The validation also exposes a practical pitfall: pre-trend tests clustered at roughly 40 industries over-reject a true null. The framework, released as open code, is ready for application to Canadian enterprise microdata, where it will inform estimates of potential output and the persistence of Canada's productivity gap.

Within-fire estimates of biomass loss across national forests of the US West Coast: inventory-informed inference with uncertainty

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05614v1 Announce Type: new Abstract: Wildfire is reshaping forests in the western United States (US), yet estimates of wildfire impacts often rely on burned-area summaries or satellite-derived severity metrics that do not directly quantify changes in forest biomass or their uncertainty. We combine US Forest Inventory and Analysis plot measurements with annual 30 m tree canopy cover data in a Bayesian spatio-temporal modeling framework to estimate within-fire changes in live aboveground biomass (AGB) and forest mortality area across National Forest System lands in Washington, Oregon, and California. The model represents both live forest presence or absence and AGB conditional on live forest, allowing posterior predictive estimates of pre- and post-fire conditions at the pixel scale. Applied to 6,239 fires from 2000 to 2022, the analysis estimates 95.3 million Mg of wildfire-associated AGB loss and 2.39 million ha of forest mortality area, with the largest aggregate impacts occurring in 2020. Pixel-level estimates reveal substantial spatial heterogeneity within fire perimeters, including large differences between total burned area, forest mortality area, and associated biomass loss. This inventory-informed, uncertainty-aware approach provides a scalable framework for quantifying forest carbon impacts of disturbance across broad regions while retaining within-fire spatial detail.

From Counting to Continuous Natural Exponential Families

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05478v1 Announce Type: new Abstract: Natural exponential families (NEFs) are characterized by their variance functions (VFs), namely by the pair $(V,M)$, where $V$ expresses the variance as a function of the mean and $M$ is the mean domain. This characterization naturally raises the inverse question: when is a given function $V$ the VF of an NEF, and what structural properties of the family can be read directly from $V$? Bar-Lev (1987), as part of a more general result for absolutely monotone functions, showed that every nonzero polynomial \[ V(m)=\sum_{j=1}^{r} a_j m^j,\qquad a_j\ge 0, \] is the VF of an infinitely divisible NEF on a positive mean domain. This polynomial class splits exhaustively into the cases $a_1>0$ and $a_1=0$. Bar-Lev, Letac and Ridder (2024) proved that, after scaling so that $a_1=1$, the first case yields a counting NEF supported on $\mathbb N_0$. We establish the complementary result: when $a_1=0$, the corresponding NEF is absolutely continuous with respect to Lebesgue measure on the positive half-line. More generally, we prove absolute continuity whenever \[ V(m)=m^2G(m), \] where $G$ is a nonzero power series with nonnegative coefficients. When $G$ is a polynomial, the mean domain is the entire positive half-line. We also record several consequences for the cumulant structure and for statistical inference.

How Long Is the Journey to Work? One-Way Commuting Time in the United States from American Community Survey Data, 2006-2024, with Travel-Diary, European and English Comparisons

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05218v1 Announce Type: new Abstract: The mean travel time to work is one of the most cited statistics of the American Community Survey (ACS), yet its distribution, its dependence on mode and departure time and its relation to other measurement bases are rarely set out together. Using ACS 1-year tables, we report that US workers aged 16 and over who did not work from home averaged 27.2 minutes one way in 2024, against 25.0 minutes in 2006, a peak of 27.6 in 2019 and 25.6 in 2021. Dividing published aggregate minutes by workers, commuter rail, long-distance train and ferry riders averaged 71.0 minutes, 2.68 times the 26.5 minutes of solo drivers, and all public transportation 49.5 minutes. In 2024, 9.3% of commuters, about 13.3 million people, travelled 60 minutes or more each way and 3.0% 90 minutes or more; commuters leaving between 5:00 and 5:29 a.m. averaged 35.1 minutes. State means ranged from 33.2 minutes in New York to 17.5 in North Dakota, and big-metro means from 36.5 minutes in New York to 21.5 in Buffalo. Working from home rose from 5.7% of workers in 2019 to 17.9% in 2021 and stood at 13.3% in 2024. The 2022 National Household Travel Survey recorded an average commute trip of 13.43 miles at 25.51 mph. On different definitions, the 2019 EU labour force survey module gave an EU average of 25 minutes and 30 minutes for the United Kingdom, and England's travel diary a commuting trip of 31.5 minutes in 2025 against 26.5 in 2002. The three bases are reported side by side and never pooled. All inputs are public.

Bayesian Markov Chain Monte Carlo-Based Simultaneous Speed Prediction Model for Heterogeneous Traffic on Urban Primary Roads

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05027v1 Announce Type: new Abstract: Objectives: The study designs a simultaneous speed prediction model based on Bayesian Markov Chain Monte Carlo (MCMC) methods for heterogeneous, non-lane-based traffic on urban primary roads, with the aim of determining the effects of vehicle-specific traffic densities on the operating speeds of the six vehicle types. Methods: The traffic data were obtained from videos recorded by unmanned aerial vehicles on five main urban roads in Dhaka, Bangladesh, and were then processed by a deep learning approach in order to derive information on vehicle trajectories, traffic volumes, densities, and space-mean speeds. Six simultaneous equations for speed prediction were developed using a Bayesian MCMC framework, covering standard cars, utility vehicles, heavy vehicles, three-wheelers, two-wheelers, and non-motorized vehicles. The performance of the models was assessed by means of goodness-of-fit measures. Findings: The coefficients of determination for the models varied from 0.922 to 0.956 and the root mean square errors were between 0.50 and 1.56 km/h for the six types of vehicle. Operating speeds decreased steadily as traffic volume increased, although traffic composition had a significant effect on speed when the demand was moderate or high. Operating speeds increased and congestion was delayed when non-motorized vehicles were excluded. The transferability study showed that the models had a reliable ability to make predictions on separate road sections.

A Markov Chain Approach to Modeling Rugby Union

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04813v1 Announce Type: new Abstract: Rugby Union's continuous play, variable-length possessions, and multiple scoring outcomes make it difficult to model with standard approaches. We present a Markov Chain framework that represents Rugby Union as a finite state space over score differential, remaining time, and pitch location, with transition probabilities estimated from historical match data. The resulting model supports simulation and analysis of in-game trajectories, including win probability and expected point estimates from any given state. We validate the model through calibration analysis and comparison to models that predict only final outcomes. Our state-space approach produces well-calibrated, competitive estimates while additionally enabling analysis of how games evolve between states.

Multi-Target Tracking of Cooperating Swarms by an Ensemble Gaussian Mixture Filter

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04127v1 Announce Type: new Abstract: Per-target labeled random-finite-set filters, such as the state of the art $\delta$-generalized labeled multi-Bernoulli filter, cannot represent cooperating, swarm-like, motion between targets. In this work, we present a new filter that can. The new particle filter couples the joint particle filter with ensemble Gaussian mixture filter such that a measurement updates the density at every particle instead of merely reweighting. We prove that the new particle filter converges to the joint particle filter in the limit of particle number and thus to the true Bayesian posterior, under certain assumptions. Experimental results on two coupled systems, the Vicsek model and coupled Brownian motion provide evidence on the efficacy of the filter.

Consistency of penalized maximum likelihood estimation for multidimensional change-in-velocity detection

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04191v1 Announce Type: new Abstract: We establish statistical consistency for the penalized maximum-likelihood estimator underlying CPLASS, a method for detecting changes in velocity in $d$-dimensional time-series data. The signal is modeled as a continuous piecewise-linear trajectory observed with independent Gaussian noise. Unlike classical change-in-mean models, continuity across adjacent segments couples their parameters and prevents direct application of standard segmentation arguments. Under compact parameter spaces, minimum segment-length and velocity-jump conditions, and a strengthened Schwarz information criterion penalty $\rho_k(\log n)^\gamma$ with $\gamma>1$, we prove joint consistency of the estimated number of segments and all changepoint locations in the high-frequency regime $n\to\infty$. The maximum changepoint-location error is $O_{\mathbb{P}}\{(\log n/n)^{1/2}\}$. The proof first uses empirical-process theory to establish convergence of the fitted signal, variance, and likelihood for each fixed model size. It then combines overfitting and underfitting arguments with a two-stage geometric localization analysis, yielding an initial $(\log n/n)^{1/3}$ rate that is sharpened by exploiting the local two-segment continuous piecewise-linear structure.

Optimal Community Recovery by Spectrally Initialized Variational EM in General Stochastic Block Models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04376v1 Announce Type: new Abstract: We prove a Chernoff-exponent guarantee for the output of spectrally initialized batch variational EM after a prescribed iteration budget, without assuming global maximization of its variational objective. The iteration repeatedly estimates the entire block probability matrix and community proportions from the same sparse graph. We consider a fixed number of communities with proportions bounded away from zero and fixed, positive, distinct connectivity profiles; neither assortativity nor full rank is required. The algorithm uses simultaneous softmax updates without sample splitting or posterior thresholding. Its analysis must control the feedback between estimated parameters, soft labels and reused edges at an exponentially small risk scale. We establish a uniform one-step bound over data-dependent soft assignments whose random remainder has exponentially small expectation. Combined with an exponentially reliable regularized spectral initializer, this yields an unconditional expected misclassification rate bounded by $\exp\{-(1-o(1))J_n\}$ throughout the sparse, diverging-degree regime, where $J_n$ is the minimum nodewise Chernoff information. Matching lower bounds establish first-order logarithmic minimax optimality on local parameter spaces allowing unknown connectivity and varying community counts. The algorithm also attains the sharp first-order exact-recovery threshold. Numerical experiments illustrate refinement gains and sensitivity to initialization and imbalance.

Network inference for SDEs with diverging dimension under small noise

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04847v1 Announce Type: new Abstract: We consider inference for network stochastic differential equations in a small-noise, high-dimensional regime, where the diffusion coefficient vanishes with $\ep\to0$ while the network size and parameter dimension may diverge. We develop a minimum-distance estimation framework based on a deterministic measurement model that may omit nuisance terms in the drift, and derive a non-asymptotic error bound decomposing the estimation error into stochastic fluctuation, nuisance discrepancy, and identifiability terms. For a linearly parametrized interaction model under repeated measurements, we obtain explicit non-asymptotic bounds on the nuisance discrepancy and the identifiability gap in terms of graph connectivity and noise level. Under suitable mixing and balance conditions, this yields consistency and convergence rates for the estimator. We further study graph recovery via adaptive Lasso. The penalized estimator is shown to inherit the rate of the preliminary estimator and to recover the true interaction graph consistently. These results provide a theoretical basis for parameter estimation and edge selection in high-dimensional network SDEs with nuisance drift components.

When Is a Graph a Covariance? Bayesian Residual Propagation under Covariance Uncertainty

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04989v1 Announce Type: new Abstract: Observing a prediction error at one node can help correct predictions elsewhere, but the benefit depends on the residual dependence between nodes. A graph suggests where that dependence might occur, yet does not establish its sign or strength. We develop a Bayesian model of residual covariance to determine how revealed errors should update a fixed feature-based predictor. For a fixed set of revealed nodes, we derive an exact identity for the change in expected squared error under linear residual propagation. The identity characterizes the optimal linear update and expresses the excess error of any other update as an exact quadratic. Under covariance uncertainty, the Bayes-optimal fixed linear update uses the posterior mean covariance. We average over four positive-semidefinite covariance families representing no dependence, positive dependence, negative dependence, and dependence whose sign can alternate with graph distance. Across eight graph benchmarks, four show posterior support within the distance-profile family for negative covariance between neighbors and alternating signs with distance. Among the evaluated methods, ours achieves the smallest worst-case recall gap to the best method on each graph. The method improves squared error over residual propagation on five of eight graphs, but performs substantially worse on one dense heterophilous graph. In these experiments, selecting the highest-posterior family performs similarly to model averaging.

Minimax estimation of the expected conditional covariance under bounds on the covariate density

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05006v1 Announce Type: new Abstract: In many scientific studies, evaluating the association between two responses requires adjusting for shared covariates. The expected conditional covariance measures this adjusted association and is used in conditional independence testing and treatment effect estimation. Researchers often estimate it using fitted conditional means, but removing the bias caused by the estimation errors of these conditional means remains a difficult task. This difficulty can increase when the true covariate density is unknown and restricted only by known upper and lower bounds. In this article, we study how accurately the expected conditional covariance can be estimated under these density bounds. We propose a multiresolution estimator that reduces bias without estimating the density. Theoretical results show that, for bounded responses and rough regression functions, an unknown density slows the optimal worst-case rate by a power of sample size compared with a known density. We establish that the optimal rate under density bounds alone strictly improves upon the previously conjectured polynomial rate by a sub-polynomial factor, resolving a long-standing conjecture. Our estimator attains this rate up to a logarithmic factor. Through simulations and a real data resampling experiment on diamonds, we show that our method can yield smaller mean squared errors than standard uncorrected estimators.

Poisson Autoregression on a Large Network with a Stochastic Block Model Structure

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05365v1 Announce Type: new Abstract: We consider multivariate Poisson autoregressive processes evolving on random networks generated by a Stochastic Block Model. This framework extends existing network Poisson autoregressions by incorporating latent community structure and allowing for non-Markovian dependence, both excitatory and inhibitory. We establish a mean-field approximation and prove that the finite system converges to its limit at the optimal rate $N^{-1/2}$ in the quenched setting with overwhelming probability, both on average and in uniform norm. Our analysis yields quantitative error bounds that are explicit in the time horizon and, under suitable stability conditions, remain polynomial or uniform in time, thereby avoiding the exponential growth typically associated with Gr\"onwall-type arguments. As a consequence, the mean-field approximation is shown to hold uniformly over any time horizon. We further demonstrate how the approximation can be exploited to reduce the computational complexity of parametric inference from $\mathcal{O}(N^2T^2)$ to $\mathcal{O}(NT^2)$. The results provide a theoretical foundation for the analysis and inference of count-valued processes on large random networks with community structure.

Measuring the roughness of a signal

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05457v1 Announce Type: new Abstract: We study the non-parametric estimation of the roughness of a path from discretely sampled observations. Our approach is based on the concept of normalized power variation of a path. The estimator identifies a variation index by comparing coarse increments with local sums of fine increments. We prove pathwise consistency under H\"older regularity, nondegenerate coarse critical power sums, uniform local bounds on fine critical power sums, and separation of the two sampling scales and obtain a convergence rate for the estimator. Neither convergence of critical variation nor monotonicity of the finite-sample statistic is required. The result applies to fractional Brownian motion under an explicit dyadic sampling rule and to Schauder series with bounded coefficients bounded away from zero. For signed Takagi--Landsberg functions we obtain a uniform asymptotic formula and a quantitative bound for every root of the estimating equation in a fixed parameter interval. We illustrate the results with numerical experiments for Takagi-- Landsberg functions and fractional Brownian motion.

Surrogate-powered Causal Inference with Censored Outcomes

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05486v1 Announce Type: new Abstract: Clinical trials with survival endpoints lose information when participants are censored before death is observed. We develop target-preserving estimators that use posttreatment disease history, such as recurrence or progression, to recover information lost to censoring for marginal survival and restricted mean survival effects. The difficulty is that the intermediate event is downstream of treatment: naive adjustment can change the causal estimand, and the useful information enters only through the observed coarsening. We derive observed-data influence functions with and without recurrence history and obtain an exact gain identity. The identity shows that efficiency improvement is driven by the censoring hazard, the split of the alive risk set into recurrence states, and the residual-survival separation between those states. In the no-covariate illness-death model, the Aalen-Johansen estimator realizes the recurrence-augmented efficient score after standardization to the marginal target. With covariates, correctly specified Cox-Breslow transition hazards provide a root-N plug-in benchmark, while a hazard-induced one-step estimator gives rate robustness and, under primitive transition and censoring learner rates, canonical inference with a second-order product remainder. A semi-synthetic metastatic breast cancer study calibrated from digitized progression-free survival and overall survival curves illustrates the gain identity. The framework applies broadly to censored time-to-event studies with informative intermediate histories.

Rank-one variance inflation in polynomial estimation of signal parameters with a sign-preserving fractional-power basis

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05511v1 Announce Type: new Abstract: The polynomial maximization method estimates signal parameters in non-Gaussian noise from a finite description of the noise by its moments and cumulants, without a density. Known accuracy results assume that these noise characteristics are known, or use a design in which estimating them jointly costs no accuracy. In practice they are estimated from the residuals of a preliminary fit, and the effect of this substitution on accuracy is unknown. We treat the feasible scheme as a two-step estimator and, for a general smooth signal model in a fixed design, find the increment of its asymptotic covariance in closed form: $\Sigma_{\rm fe}-\Sigma_{\rm or}=c_2(1-g_{\rm or}) Q^{-1}\bar{d}\bar{d}^{\top}Q^{-1}$, a positive semidefinite matrix of rank at most one. Here $c_2$ is the noise variance, $g_{\rm or}\le 1$ the oracle variance reduction factor, and $Q$ and $\bar{d}$ the second-moment matrix and mean of the signal gradient over the design. Estimating the fractional moments that form the weights costs no first-order accuracy, because that block is orthogonal; the whole increment comes from estimating the sign-preserving centering means. The increment lies along the single direction $Q^{-1}\bar{d}$, so linear combinations of the parameters orthogonal to it keep oracle accuracy. In the trace metric the variance reduction factor becomes $g_{\rm fe}=g_{\rm or}+(1-g_{\rm or})R_D$, where $R_D=\|Q^{-1}\bar{d}\|^2/{\rm tr} Q^{-1}$ depends on the design alone. We give four sufficient conditions for first-order oracle equivalence; noise symmetry is not among them. Monte Carlo experiments with a harmonic signal confirm the direction and size of the increment. A covariance estimate that ignores the increment undercovers where non-Gaussianity gives the largest gain, symmetric noise included.

Exact finite-sample bias, variance, and MSE of normalized scale-invariant inequality indices under Gamma mixture models

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05621v1 Announce Type: new Abstract: We study the finite-sample properties of estimators of a broad class of normalized scale-invariant inequality indices (NSIIs) under finite Gamma mixture models. The class includes the Gini coefficient, the $m$th Gini index, the Extended $m$th Gini index, linear order-statistic inequality indices, and several entropy- and dispersion-based measures. Building on the Gamma--Dirichlet representation, we derive exact expressions for the expectation and finite-sample bias of the natural estimator of an NSII based on a $U$-statistic when the population follows a finite Gamma mixture with a common rate parameter. The resulting bias formula explicitly characterizes the effects of the mixture weights and component shape parameters. We also establish that the bias converges to zero as the sample size increases, yielding asymptotic unbiasedness. Furthermore, we derive exact finite-sample expressions for the variance and mean squared error of the estimator by accounting for the overlap structure among the subsets entering the $U$-statistic. In addition, we establish strong consistency and asymptotic normality. When the mixture degenerates to a single Gamma distribution, the finite-sample bias vanishes, recovering the exact unbiasedness result previously obtained for NSIIs under the Gamma model. Numerical illustrations and simulation studies are provided to investigate the finite-sample behavior of the estimator and to illustrate the theoretical findings. Overall, the proposed framework provides a unified characterization of finite-sample estimation under heterogeneous Gamma populations and quantifies the effects of mixture heterogeneity on bias, variance, and mean squared error.

Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05864v1 Announce Type: new Abstract: We construct a feasible two-step estimator for the elasticity parameter in small-noise CEV-type diffusions. Under joint small-noise and high-frequency asymptotics, we establish its consistency and an $\varepsilon^{-1}$ central limit theorem with an explicit asymptotic variance. We adapt a Lamperti-based transformation strategy to elasticity inference for a CEV process with an attainable, absorbing $0$ boundary. Under a local-to-CEV scaling, an auxiliary CKLS process and a Girsanov change of measure yield a strictly positive CIR-type benchmark in which the elasticity is recast as a linear-drift parameter. A preliminary elasticity estimator based on local realized variance supplies the unknown parameter in the state mapping, yielding a feasible LSE-type estimator. The asymptotic theory combines control of the CKLS-to-CEV path-replacement error, total-variation closeness between the original and changed measures, and asymptotic negligibility of the preliminary plug-in error, thereby transferring the auxiliary CIR limit theory to the feasible estimator under the original measure.

Learning Sparse Support under Differential Privacy: Adaptive Algorithms and Minimax Limits

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05867v1 Announce Type: new Abstract: We study exact support recovery under $(\epsilon,\delta)$-differential privacy in sparse high-dimensional linear regression. We introduce Saturated Propose-test-release, a general mechanism that privately releases the output of a discrete selector with probability one once its stability certificate reaches a finite threshold. Exploiting the coordinatewise geometry of the LASSO, we construct a computable support-stability score. The resulting computationally efficient Saturated LASSO satisfies worst-case $(\epsilon,\delta)$-differential privacy and achieves exact support recovery with high probability under explicit regularity and beta-min conditions. Maximizing sparsity-indexed certificates yields an adaptive procedure requiring no sparsity knowledge and having exactly the same finite-sample exact-recovery risk as the oracle fixed-sparsity procedure under common public tuning parameters. We also establish a minimax lower bound explicitly tracking $\delta$: under its recovery conditions, Saturated LASSO is minimax optimal up to logarithmic factors in $n$ and $1/\delta$ uniformly over $0 < \delta \leq \epsilon/16$; in the broad moderate-$\delta$ regime, it further matches the lower-bound $\delta$-dependence. A complementary information-theoretic construction with known sparsity attains the lower-bound rates up to constant factors under independent Gaussian design, at exponential computational cost. Simulations and a semi-synthetic study using public American Community Survey covariates illustrate the numerical performance of the proposed procedures.

Bradley-Terry model under general comparison graphs

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06237v1 Announce Type: new Abstract: The Bradley-Terry model is a parametric model for ranking from pairwise comparisons. Existing asymptotic theory for the maximum likelihood estimator (MLE) in regimes where the number of objects grows often requires homogeneity assumptions or compatibility conditions on comparison graphs, which limits its applicability to many practical settings. In this work, we establish uniform consistency of the MLE under general deterministic comparison designs. Our pairwise error bound consists of a pair-specific term governed by the effective resistance between the corresponding objects and a global term governed by the spectral gap of the unnormalized graph Laplacian. The bound is tight up to logarithmic factors for certain graph sequences. For any prespecified sequence of pairs satisfying an additional balancing condition, we further establish asymptotic normality of the corresponding estimated utility differences. As an application, we obtain uniform consistency for independent-edge random graph designs whenever the minimum edge probability exceeds the Erd\H{o}s-R\'enyi connectivity threshold by a logarithmic factor, as well as asymptotic normality under additional balancing conditions.

Sharp dimensional analysis of midpoint methods for Langevin sampling

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.06308v1 Announce Type: new Abstract: We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target $\pi \propto e^{-V}$, where $0 \prec \alpha I\preceq\nabla^2V\preceq\beta I$ and $\kappa=\beta/\alpha$. To achieve $\sqrt\alpha\,W_2\leqslant\varepsilon$, we show that deterministic Heun uses at most $\widetilde O(\kappa^{4/3}d^{1/3}\varepsilon^{-2/3})$ gradient queries, and underdamped exponential midpoint uses $\widetilde O(\kappa^{5/4}d^{1/4}\varepsilon^{-1/2})$. The proofs exploit cancellation at stationarity and smoothing using techniques from Malliavin calculus, outperforming previous upper bounds based on standard couplings. At bounded condition number, a lower bound matches the $d$ and $\varepsilon$ powers of both deterministic methods. To contrast, for the randomized midpoint methods and Poisson midpoint with at least two grid points (both overdamped and underdamped variants), a simple Gaussian calculation yields a lower bound $d^{1/3}\varepsilon^{-1/3}$ to get an $\varepsilon$-close sample despite starting at a benign initialization. This shows surprisingly that in high dimensions, deterministic discretizations can outperform their random counterparts.

In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2510.10981v3 Announce Type: cross Abstract: This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We introduce a principled risk decomposition that separates the total ICL risk into two orthogonal components: Bayes Gap and Posterior Variance. The Bayes Gap quantifies how well the trained model approximates the Bayes-optimal in-context predictor. For a uniform-attention Transformer, we derive a non-asymptotic upper bound on this gap, which explicitly clarifies the dependence on the number of pretraining prompts and their context length. The Posterior Variance is a model-independent risk representing the intrinsic task uncertainty. Our key finding is that this term is determined solely by the difficulty of the true underlying task, while the uncertainty arising from the task mixture vanishes exponentially fast with only a few in-context examples. Together, these results provide a unified view of ICL: the Transformer selects the optimal meta-algorithm during pretraining and rapidly converges to the optimal algorithm for the true task at test time.

An inverse-stochastic-control Galerkin estimator for drift potentials

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04268v1 Announce Type: cross Abstract: We consider the ill-posed inverse problem of recovering the drift potential of an overdamped Langevin diffusion from discrete, possibly irregular position observations. Specializing the suboptimality gap for inverse stochastic control to drift-potential recovery, we parametrize the associated value function in a finite basis. Under a basis nondegeneracy condition, the resulting Galerkin estimator is obtained from one positive-definite linear system whose entries are smooth functionals of the empirical time marginals; no transition density is required. The gap equals one half of the squared energy distance to the true potential, yielding a best-approximation identity and energy-seminorm consistency as the basis becomes complete. At a fixed basis, we separate the sample fluctuation from the time-quadrature error, thereby avoiding the Euler--Maruyama $O(\Delta t)$ drift-discretization bias. We also analyze the finite basis as regularization, give a dimension-dependent convergence rate for a concrete basis family, and bound observation-noise bias. One- and two-dimensional experiments verify the predicted sampling-interval behavior. An application to irregular animal telemetry illustrates the method on a single long trajectory.

Efficient Mass Matrix Estimation with Gaussian Cooling

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.04806v1 Announce Type: cross Abstract: We introduce an algorithm for efficiently preconditioning log-concave and log-smooth distributions that scales logarithmically with the condition number of the underlying distribution. Based on Gaussian cooling, our multistage method approximately samples from a sequence of well-conditioned distributions to construct a preconditioner for each subsequent stage of the cooling schedule. This method is motivated by existing practical approaches for mass matrix estimation in Markov chain Monte Carlo (MCMC), in which an effective preconditioner for the target distribution is estimated from samples produced during a warm-up period. However, our approach is conceptually distinct from existing approaches and moreover permits theoretical analysis. Our algorithmic framework is flexible, allowing essentially any log-concave sampling algorithm to act as the subroutine within each cooling stage. For instance, using first-order rejection sampling (FORS) as the sampler, the first-order query complexity of our method is $\tilde{O}(d^{4/3} \log \kappa)$ for a large class of log-concave and log-smooth distributions with condition number $\kappa$ and $\tilde{O}(d^{1/3} \log \kappa)$ for translation-invariant distributions. In the translation-invariant setting, we provide numerical experiments for the lattice $\phi^4$ model, a simple lattice field theory.

A Statistical Inference Framework for PMI Estimation and SGNS Word Embeddings

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05058v1 Announce Type: cross Abstract: Pointwise Mutual Information (PMI) is a core measure of testing word association, and Skip-gram with Negative Sampling (SGNS) is essentially a method that implicitly factorizes a shifted PMI matrix. However, a systematic and well-rounded characterization of finite-sample uncertainty in PMI estimation remains absent and imperative to venture into. We provide a statistical framework for PMI estimation and its connection to SGNS. We prove consistency, asymptotic unbiasedness, and asymptotic normality of the empirical PMI estimator, derive its variance via the Delta method, and, applying stochastic approximation theory, obtain a variance decomposition for SGNS-based PMI estimation that separates data variance from optimization variance. Simulation experiments validate the Delta method approximation. Real-data experiments on the Brown Corpus (d = 100) reveal that SGNS systematically deviates from the theoretical relationship PMI + log K. The empirical relationship shows an attenuated PMI coefficient, an amplified log K effect, and a positive intercept, indicating systematic bias. Word analogy validation confirms the models are effective. The failure to validate the variance decomposition under low-dimensional conditions does not diminish its theoretical value; rather, it identifies the unbiasedness assumption as the key bottleneck and clarifies the gap between asymptotic theory and practice, providing implications for both practice and theory.

Regression models for ordinal compositional data

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.05212v1 Announce Type: cross Abstract: We present a unified, transformation-free linear regression framework tailored for ordinal compositional data, such as distributions across educational levels or aggregate Likert-scale survey responses. Traditional log-ratio approaches often obscure interpretability, ignore the inherent ordering of categories, and struggle with boundary zero values. To overcome these limitations, we propose a deterministic model constrained to the space of column-stochastic transformation matrices, naturally preserving the fundamental geometry of the simplex. By adopting the weighted 1-Wasserstein distance as the loss function, our method directly embeds the ordinal nature of the data into the estimation process. We provide a computationally efficient and globally optimal solution explicitly formulated as a Linear Programming (LP) problem. The framework systematically addresses four distinct regression scenarios, introducing a novel ordinal tensor product to rigorously handle interactions across multiple compositional predictors. Furthermore, we equip the model with a suitable regularization strategy and novel diagnostic tools, including a Wasserstein-based coefficient of determination ($R^2_W$) and an Order Preservation Index (OPI). Extensive simulation studies and two empirical applications demonstrate the robust predictive performance and interpretability of the proposed methodology.

Latent Score-Based Bayesian Cram\'er-Rao Bound Estimation for High-Dimensional Imaging Systems

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2610.03956v1 Announce Type: new Abstract: We propose a data-driven framework for estimating the Bayesian Cram\'er-Rao bound (CRB) in high-dimensional imaging systems with complex, analytically intractable priors. Direct CRB computation is challenging in this setting due to the need to model the prior score and to form and invert the Bayesian Fisher information matrix in very high dimensions. To address these issues, we first reformulate the inverse problem in the latent space of a pre-trained variational autoencoder, thereby dramatically reducing the dimensionality of the bound estimation problem while preserving the spatial structure of the images. The Bayesian CRB is formed in this latent space and mapped back to the native parameter space using a change-of-variables formula. Second, to learn the latent prior score, we introduce a new sliced score matching objective defined in a Bochner space endowed with an $H^1(\Omega)$ Sobolev norm in space. This "Bochner-space sliced score matching" objective is consistent with standard sliced score matching, but penalizes errors in the spatial gradients of the score, suppressing high-frequency artifacts that otherwise contaminate the resulting CRB estimates. We validate the approach on a stylized quantitative photoacoustic computed tomography (qPACT) breast imaging problem with over one million unknown parameters, using a foundation-model autoencoder derived from Stable Diffusion. The proposed method yields stable, artifact-free Bayesian CRB estimates that reflect the highly non-Gaussian structure of the learned prior and reveal the substantial impact of the prior on the relative performance of competing qPACT design schemes.

A friendly introduction to triangular transport

Tue, 06 Oct 2026 00:00:00 -0400

arXiv:2503.21673v2 Announce Type: replace Abstract: Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box models, however, these representations are rarely known. We discuss how to characterize and manipulate such representations using triangular transport maps, which approximate any complex probability distribution as a transformation of a simple, well-understood distribution. The particular structure of triangular transport guarantees many desirable mathematical and computational properties that translate well into solving practical problems. Triangular maps are actively used for density estimation, (conditional) generative modelling, Bayesian inference, data assimilation, optimal experimental design, and related tasks. While there is ample literature on the development and theory of triangular transport methods, this manuscript provides a detailed introduction for scientists interested in employing measure transport without assuming a formal mathematical background. We build intuition for the key foundations of triangular transport, discuss many aspects of its practical implementation, and outline the frontiers of this field.

Bifidelity Karhunen-Lo\`eve Expansion Surrogate with Active Learning for Random Fields

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2511.03756v2 Announce Type: replace-cross Abstract: We present a bifidelity Karhunen--Lo\`{e}ve expansion (KLE) surrogate model for field-valued quantities of interest (QoIs) under uncertain inputs. The QoIs considered here are scalar fields. The approach combines the spectral efficiency of the KLE with polynomial chaos expansions (PCEs) to preserve an explicit mapping between input uncertainties and output fields. By coupling inexpensive low-fidelity (LF) simulations that capture dominant response trends with a limited number of high-fidelity (HF) simulations that correct for systematic bias, the proposed method can enable accurate and computationally affordable surrogate construction. To further improve surrogate accuracy, we develop an active learning strategy that adaptively selects new HF evaluations based on the surrogate's generalization error, estimated via cross-validation and modeled using Gaussian process regression. New HF samples are then acquired by maximizing an expected improvement criterion, targeting regions of high surrogate error. The resulting BF-KLE-AL framework is demonstrated on three examples of increasing complexity: a one-dimensional analytical benchmark, a two-dimensional convection-diffusion system, and a three-dimensional turbulent round jet simulation based on Reynolds-averaged Navier--Stokes (RANS) and enhanced delayed detached-eddy simulations (EDDES). The experiments show that bifidelity gains depend on LF accuracy, discrepancy approximation, and the allocation of simulation cost. Active learning improves prediction over random sampling in several settings, while the cost-matched comparisons identify both favorable regimes and cases where an HF-only surrogate is more accurate.

Cellwise, Blockwise, and Casewise Robust Multiblock PCA for Sustainable and Inclusive Wellbeing in the EU

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03181v1 Announce Type: cross Abstract: Gross Domestic Product (GDP) is widely used to guide economic and social decision-making, but it provides only a partial view of wellbeing. For this reason, the European Union (EU) has launched initiatives to monitor sustainable and inclusive wellbeing beyond GDP, developing indicator frameworks that cover dimensions such as health, education, environment, and social inclusion. These indicators are naturally grouped into thematic areas, and policymakers are interested in understanding how these areas contribute to global wellbeing and which indicators explain differences across countries. However, such data are high-dimensional, contain missing values, and may include anomalies affecting entire observations, specific thematic areas, or individual indicators. We introduce blockwise outliers and propose bloccPCA, a robust multiblock PCA method that simultaneously handles casewise, blockwise, and cellwise outliers, as well as missing values. The method provides robust global components to summarize the overall structure of wellbeing, while preserving thematic-area contributions through robust blockcomponents. It also yields diagnostic tools to identify whether anomalies arise at the case, block, or cell level. Monte Carlo simulations and an application to the EU wellbeing dataset show that bloccPCA provides valuable insights into sustainable and inclusive wellbeing.

Bayesian Analysis of Covariate-Driven Hawkes Processes with Application in Plant Epidemiology

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03189v1 Announce Type: cross Abstract: Hawkes processes are widely used to model temporal point patterns exhibiting self-exciting behavior. In this work, we consider a Hawkes model with a baseline intensity depending on a set of dynamic covariates and an exponential triggering function. A Bayesian approach is applied to variable selection in this context. Spike-and-slab priors are proposed to enable a parsimonious choice of relevant variables. We also provide practical simulation procedures for the fitted covariate-driven Hawkes model, which support posterior predictive checks and probabilistic forecasting. This approach is illustrated by the example of spore release of Venturia inaequalis, the fungus responsible for apple scab disease. We study the dependence of primary spore releases on environmental covariates and highlight the self-exciting behavior of subsequent releases. The Bayesian framework also provides a natural basis to forecast future spore releases. By delivering interpretable posterior inclusion probabilities alongside uncertainty-aware predictive risk bands, this new methodology provides a rigorous foundation for managing temporal event risks driven by both external environmental forcing and internal contagion.

Jagged AI in Scientific Peer Review: Evidence from POMP Data Analysis

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2605.07855v3 Announce Type: replace Abstract: Despite their growing use in academic writing and statistical analysis, the performance of artificial intelligence (AI) tools in scientific peer review remains a largely unexplored area. A key challenge is jagged AI, a phenomenon where AI exhibits strong ability spikes in some domains while remaining deficient in others. To study this jaggedness in a practical data science context, we considered the task of reviewing partially observed Markov process (POMP) data analyses. POMP models, a generalization of state-space models or hidden Markov models, are used to fit mechanistic dynamic models to time series data in diverse applications including disease transmission, ecological dynamics, and financial risk assessment. High-quality peer review in this area entails assessment of scientific context, identification of errors in implementing complex algorithms, and decisions concerning methodological best practices. We studied 72 POMP projects from four semesters of a University of Michigan graduate time series course for which the project reports, the source code, and student peer reviews are anonymized and open access. We compared the human reviews with four AI review agents, using Claude Code with differing instructions implemented as skill files. We found that the AI review agents exhibited a jagged capability profile, identifying plausible technical errors and instances of invalid inference methodology overlooked by humans, while showing lower capability at finding issues involving interpretive errors, narrative coherence, and domain-informed model critique. The jaggedness was similar for all agents, consistent with other research finding that the specific instructions can have limited effect on the capability of AI models for some tasks. Skill file configuration shifted which weaknesses agents emphasized, without removing the jaggedness.

Hybrid Models for Short-Term Sea-Level Forecasting

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.29827v2 Announce Type: replace Abstract: Accurate tide forecasts are essential for coastal management, navigation, flood-risk reduction, and infrastructure protection. Observed sea level can be decomposed into astronomical and non-astronomical components, the latter mainly driven by meteorological effects. This study investigates a hybrid framework for hourly sea-level forecasting that combines harmonic analysis (HA) for the astronomical component with data-driven models for the non-astronomical contribution. The approach is evaluated at six tide-gauge stations with different tidal regimes: Venice, Trieste, Saint-Malo, Vard{\o}, Nikiski, and Nagasaki. Four data-driven model classes are considered: (i) linear parametric models, represented by autoregressive models with exogenous variables; (ii) functional parametric models, based on functional autoregressive models with exogenous variables; (iii) semiparametric and nonlinear models, including generalized additive models and autoregressive neural networks; and (iv) a semi-functional non-standard k-nearest-neighbours approach combining similarity in recent non-astronomical trajectories and meteorological conditions. Results reveal that hybrid models reduce forecast errors by 52.9-54.9% on average relative to HA. The generalized additive model is the most competitive across locations, while k-nearest neighbours performs best at Saint-Malo and the autoregressive model with exogenous variables is favoured in Nagasaki. For Venice, an economic decision-making case study assesses the operational use of sea-level forecasts in managing the MoSE flood-barrier system.

Assessing the impact of climate change and rising temperatures on life insurance portfolios

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.32304v3 Announce Type: replace Abstract: Climate change may materially affect long-term life insurance liabilities by altering both the level and seasonal pattern of mortality. This article develops a multi-population mortality framework that combines a Hermite spline model with a distributed lag non-linear model to capture age-, region-, and temperature-specific mortality effects. We apply the framework to mortality and temperature data from 15 Spanish NUTS-2 regions and project future mortality under three shared socioeconomic pathway (SSP) scenarios. We then assess the implications for a hypothetical whole life insurance portfolio through expected death-benefit payments and portfolio profit and loss. The results reveal an important seasonal offset: warmer conditions reduce expected payoffs during winter periods but increase them during summer periods, with these effects becoming more pronounced under more severe climate scenarios and for policies issued in later years. Over longer horizons, adverse summer mortality effects become increasingly important. The portfolio analysis further shows that climate-related mortality risk can materially increase the dispersion and downside risk of portfolio outcomes, particularly under SSP5-8.5. These findings highlight the importance of incorporating temperature-related mortality effects into long-term life insurance liability projections and risk assessment.

Concave Processes for Multi-Task Career Trajectories: Evaluating Aging Across Multiple Measures of NBA Performance

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.33752v2 Announce Type: replace Abstract: NBA athlete performance tends to increase through early career as athletes develop and acclimate to the league, followed by decline due to age-related deterioration in athleticism. While this general pattern persists, the precise shape of this trajectory varies by athlete and across different measures of performance. To model performance increase and decline, we introduce the concave process prior, a novel nonparametric prior over concave functions. We then use a latent variable model to characterize dependence in aging profiles across player-metrics, embedding each player in a shared low-dimensional latent space so that players with similar profiles learn similar trajectory shapes, peak ages, and peak values. Posterior analysis of the learned embedding supports latent-space nearest-neighbor retrieval of career-comparable players and informed projections of young players. We apply our model to data across over a dozen performance metrics for over two thousand players in seasons ranging from 1997 to 2026. Our results show that jointly modeling all metrics improves held-out predictive performance over single-metric alternatives, and that the concavity constraint itself improves prediction. We find that athleticism-driven metrics such as blocks and offensive rebounds peak in a player's early twenties, while skill-based shooting metrics peak in the mid-twenties or later.

Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2504.18629v2 Announce Type: replace-cross Abstract: Racial disparities in recidivism remain a persistent challenge, and the growing adoption of risk assessment algorithms has intensified the scrutiny of their sources. Past works have primarily focused on disparities in the predictions of these algorithms, viewing recidivism as a binary outcome. While sociological and criminological research has long documented non-algorithmic factors in recidivism, it remains unclear whether the risk assessments that decision-makers act on fully account for racial disparities. This work presents a multi-stage causal framework for time-to-recidivism that captures the interactions between race, the risk assessment algorithm, and contextual factors. We introduce interventional racial parity and a formal survival analysis test, conducted with observational data, of whether the algorithmic risk assessment fully accounts for racial differences in recidivism. Applied to the COMPAS dataset, the test detects no racial disparity within risk groups at short follow-up horizons. A statistically significant disparity becomes detectable after roughly nine months in the low-risk group and persists under finer score stratification, risk score perturbation, and a competing-risks analysis. This suggests that factors beyond the algorithmic scores, possibly including structural disparities in housing, employment, and social support, may shape recidivism over time, underscoring the need for policy interventions beyond algorithmic improvements, particularly for low-risk defendants.

Self-Tuned Rejection Sampling within Gibbs and a Case Study in Small Area Estimation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2509.17155v3 Announce Type: replace-cross Abstract: When formulating a Gibbs sampler, some conditionals may be unfamiliar distributions without well-known variate generation routines. Rejection sampling may be used to draw from such distributions exactly; however, it can be challenging to obtain practical proposal distributions. A practical proposal is one where accepted draws are not extremely rare occurrences and which is not too computationally intensive to use repeatedly within the Gibbs sampler. Consequently, approximate methods such as Metropolis-Hastings steps tend to be used in this setting. This work revisits the vertical weighted strips (VWS) method of proposal construction from arXiv:2401.09696 for univariate conditionals within Gibbs. VWS constructs a finite mixture based on the form of the target density and provides an upper bound on the rejection probability. The rejection probability can be reduced by refining terms in the finite mixture. Na\"{i}vely constructing a new proposal for each target encountered in a Gibbs sampler can be computationally impractical. Instead, we consider proposal distributions which persist over the Gibbs sampler and tune themselves gradually to avoid very high rejection probabilities while discarding mixture terms with low contribution. We explore a motivating application in small area estimation, applied to the estimation of county-level population counts of school-aged children in poverty. Here, a Gibbs sampler for a Bayesian model of interest includes a family of unfamiliar densities to be drawn for each observation in the data. Self-tuned VWS is applied to obtain exact draws within Gibbs while keeping the computational workload of proposal maintenance under control.

Error Propagation in Dynamic Programming: From Stochastic Control to American Option Pricing

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2509.20239v2 Announce Type: replace-cross Abstract: This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

The Whittle likelihood for mixed models with application to groundwater level time series

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2512.20810v2 Announce Type: replace-cross Abstract: Understanding the processes that influence groundwater levels is crucial for forecasting and responding to hazards such as groundwater droughts. Mixed models, which combine a fixed mean, expressed using independent predictors, with autocorrelated random errors, are used for inference, forecasting and filling in missing values in groundwater level time series. Estimating parameters of mixed models using maximum likelihood has high computational complexity. For large datasets, this leads to restrictive simplifying assumptions such as fixing certain free parameters in practical implementations. In this paper, we propose a method to jointly estimate all parameters of mixed models using the Whittle likelihood, a frequency-domain quasi-likelihood. Our method is robust to missing and non-Gaussian data and can handle much larger data sizes. We demonstrate the utility of our method both in a simulation study and with real-world data, comparing against maximum likelihood and an alternative two-stage approach that estimates fixed and random effect parameters separately.

Assessing the Impact of Intercurrent Events on Power and Sample Size for Estimands with Time-to-Event Endpoints

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2606.03863v3 Announce Type: replace-cross Abstract: The precise definition of a primary estimand, accounting for intercurrent events (IEs) as per the ICH E9(R1) addendum, is fundamental to the design and interpretation of clinical trials. Conventional power and sample size calculations, however, often do not adequately incorporate the impact of IEs and their corresponding handling strategies, creating a risk of over- or under-powered studies. While simulation-based approaches can address this complexity, they are often computationally intensive and may only explore a limited set of scenarios. In this paper, we introduce a set of formulae for calculating power for estimands with time-to-event endpoints. We focus on estimands that use treatment policy, hypothetical, composite, or a combination of strategies for handling IEs, assuming constant hazards and that a participant's risk of experiencing an IE is unrelated to their risk of other IEs or the primary endpoint, while the effect of an IE on the endpoint is determined by the chosen handling strategy. Simulation is used to assess the accuracy of calculated power in a variety of settings, and we explore deviations in power estimates in scenarios where event times for outcomes and IEs are dependent, hazards are non-constant, or follow-up times vary. We illustrate the practical application of our approach through a case study in nasal polyposis, examining the sensitivity of sample size requirements to varying IE rates and their impacts on post-IE outcomes. The proposed formulae facilitate rapid and accurate power and assurance calculations, enabling clinical trial designs to be more closely aligned with the estimand of interest.

[EDGE] A grouped calibration test for logistic regression that tolerates a few corrupted records

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2608.20511v2 Announce Type: replace-cross Abstract: The Hosmer-Lemeshow calibration test groups patients by predicted risk for a valid reference and loses power that more groups cannot recover. Later tests weight each record's residual alone, which makes them fragile: on an otherwise correct model, one record in a thousand with a corrupted covariate raises the false-alarm rate of Stukel's score test from 5% to 12%, and ten to 63%. Pooling on equal-size groups bounds a wrong record's influence, dividing its residual by its groupmates' variance; without pooling, the same directions are as fragile as Stukel's test after a refit. EDGE, the test proposed here, projects the grouped residuals onto a small basis of calibration shapes. Its degrees of freedom do not depend on the number of groups, so the partition becomes a setting, fine-grained for power and coarse when records may be wrong, and its reference needs no resampling. In a prespecified simulation EDGE was comparable in power to Stukel's test on clean data and 0.064 more powerful on average than the ten-group Hosmer-Lemeshow test. With one and ten exaggerated covariates in a thousand its false-alarm rates were 0.056 and 0.097, and with ten groups below 0.10 up to about ten exaggerated or five reversed. In external validation, at ten groups, its average power was that of Cox's recalibration test and the GiViTI belt, and its false-alarm rate stayed below 0.10 with ten reversed records in a thousand, where theirs did not. In a 70,000-patient cohort its verdict did not change with the partition.

DOMIC: Provably Calibrated Detection of Dependence-Structure Change Points via Density-Operator Mutual Information

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.02787v2 Announce Type: replace-cross Abstract: Dependence can change between variable blocks without changing correlation; serial dependence complicates calibration. We propose DOMIC, a rank-based detector using density-operator mutual information (DOMI). Unit-norm random features make sample-level partial traces exact, so prefix sums compute segment statistics at per-split cost independent of segment length; a Gram form uses the exact kernel. Permutation tests are finite-sample exact under pair or block exchangeability for windows and schemes fixed in advance; validity after data-driven scheme selection is unproved. For i.i.d. pairs with feature dimension, frequency draw and bandwidth fixed, we prove a weighted chi-square limit at independence for the rank-based random-feature statistic. An additive entropy cost with Holevo gains drives segmentation. DOMI attains higher localised power than rank, copula, kernel and distance baselines in most non-Gaussian and correlation-free settings; the Gram form leads or ties in all 16 non-Gaussian settings where any statistic exceeds 0.10. On a three-break benchmark, Holevo partitioning returns exactly three breaks in 47.5% of replicates, against at most 19% for calibrated baselines. Block-calibrated primary scans reject in all three pre-specified pairs of a US financial panel, with strongest stage-two evidence for stocks and Treasury yields. One of 27 weather candidates passes the multiplicity-corrected re-test; candidate selection is unadjusted.

A Framework to Quantify the Probability of Future Cyber Loss Events

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.21717v2 Announce Type: replace-cross Abstract: Cybersecurity risk quantification remains challenging due to limited operational data and difficulties in quantifying Loss Event Frequency (LEF). This paper introduces the Loss Event Frequency Security Analyser (LEFSA), a probabilistic framework that reformulates LEF estimation as machine-level Cyber Loss Event (CLE) prediction combined with hierarchical infrastructure-level aggregation. LEFSA estimates calibrated machine-level CLE probabilities from operational cybersecurity telemetry and aggregates them across infrastructure layers while accounting for machine-level dependencies. This provides a foundation for scalable, explainable, and operationally applicable cyber risk estimation at the level of machines, services, business processes, and the entire organization. The framework was evaluated using proprietary Managed Detection & Response telemetry from 23 organizations using Microsoft Defender for Endpoint. XGBoost achieved the strongest predictive performance, with a mean area under the receiver operating characteristic curve of 0.90 and consistently low calibration error across evaluation periods. The results demonstrate that operational cybersecurity telemetry contains substantial predictive information for future CLE occurrence, supporting probabilistic machine-level modeling and hierarchical aggregation as a promising foundation for quantitative, data-driven cyber risk management.

Ready for the Clinic? A Survey of Open-Source Software for Response-Adaptive Randomization in Clinical Trials

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.35939v2 Announce Type: replace-cross Abstract: Response-adaptive randomization (RAR) modifies treatment allocation probabilities during a clinical trial as response/outcome data accumulate, with the aim of improving patient benefit, statistical efficiency, or both. Despite substantial methodological development, adoption of RAR in clinical practice has remained limited, and the software available to support its design and implementation has not previously been reviewed. We identified 16 publicly available, open-source software packages implementing RAR methods, spanning urn-based, target-allocation, Bayesian, Markov decision process (MDP)-based, and dose-finding approaches, and evaluated them with respect to their methodological and practical characteristics. We found that while several software packages exist, most are method-specific, and only a small number provide broader, general-purpose adaptive-trial design and analysis capabilities. Explicit support for practically relevant features, including delayed and missing outcome data, temporal trends in response rates, flexible operating-characteristic evaluation, and platform or multi-arm multi-stage trial designs, is rare or absent across the identified software. These findings suggest that while a diverse set of tools exists for exploring RAR designs, gaps remain between the methodological literature and the software available to implement it in practice. Continued development of flexible, practically oriented, and validated software is important for the wider adoption of RAR in clinical research, and we highlight interesting areas of further work.

Learning to Price Electricity for Optimal Demand Response

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.00755v2 Announce Type: replace-cross Abstract: There is considerable interest in using time-varying electricity prices to shape consumer demand response, and better align energy demand with renewable production. However, optimal prices generally vary over time in response to complex signals such as weather forecasts, sunrise/sunset times, and day-of-week patterns; and existing methods are not able to make efficient use of such rich contextual information. Here, we propose a neural-network-based algorithm for contextual energy pricing, modeling pricing as a Stackelberg game and leveraging a mean-field solution representation from Mehrabi et al.(2024). The approach learns constrained mappings from contextual features to feasible price signals. We validate our approach by simulating the energy grid in several US cities, and show that incorporating contextual information can considerably increase the value of the demand response programs.

A fast non-reversible sampler for Bayesian mixture models

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2510.03226v2 Announce Type: replace Abstract: Mixtures models are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to converge when the number of observations $n$ is large. In this paper we introduce a novel and simple non-reversible sampling scheme for Bayesian mixture models (with fixed or varying number of components), which is shown to drastically outperform classical samplers in many scenarios of interest, especially during convergence phase and when components in the mixture have non-negligible overlap. At the theoretical level, we show that the performance of the proposed non-reversible scheme cannot be worse than the standard one, in terms of asymptotic variance, by more than a factor of four; and we provide a scaling limit analysis suggesting that the non-reversible sampler can reduce the convergence time from O$(n^2)$ to O$(n)$. We also discuss why the statistical features of mixture models make them an ideal case for the use of non-reversible discrete samplers.

Optimal Quantum Speedups for Repeatedly Nested Expectation Estimation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2602.08120v2 Announce Type: replace-cross Abstract: We study the estimation of repeatedly nested expectations (RNEs) with a constant horizon (number of nestings) using quantum computing. We propose a quantum algorithm that achieves $\varepsilon$-error with cost $\tilde O(\varepsilon^{-1})$, up to logarithmic factors. Standard lower bounds show this scaling is essentially optimal, yielding an almost quadratic speedup over the best classical algorithm. Our results extend prior quantum speedups for single nested expectations to repeated nesting, and therefore cover a broader range of applications, including optimal stopping. This extension requires a new derandomized variant of the classical randomized Multilevel Monte Carlo (rMLMC) algorithm. Careful de-randomization is key to overcoming a variable-time issue that typically increases quantized versions of classical randomized algorithms.

A Semiparametric Nonlinear Mixed Effects Model with Penalized Splines Using Automatic Differentiation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2603.11728v2 Announce Type: replace-cross Abstract: We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed model representation of penalized splines, the level of smoothness can be estimated jointly with other variance components. The integration over random effects needed to obtain the marginal likelihood is carried out using the Laplace approximation. Exact derivatives for evaluation and maximization of the resulting likelihood are obtained via automatic differentiation implemented through Template Model Builder. In simulation studies, the method produces improved inferential performance and reduced computational burden when compared to the existing procedures. The approach is further illustrated through a case study on infant height growth in the first two years of life.

[DeepGOF] Where Does a Logistic Risk Model Fail? An Audited Neural Goodness-of-Fit Test for Model Development and External Validation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.29575v2 Announce Type: replace-cross Abstract: Goodness-of-fit tests for logistic regression are routine in clinical risk modelling, yet the classical tests say whether a model misfits, not where. A pretrained network is not a test until its level, power and blind spots are established. We audit DeepGOF-1, which renders the residuals of a fitted logistic model as a map over the ranks of two covariates, scores the map with a frozen convolutional network, and calibrates the score by the analyst's parametric bootstrap. The level is first-order valid under standard bootstrap regularity and two conditions, consistency against a named alternative is decided by one forward pass, and local power has an explicit limit. In simulation the level holds from 20 patients to 8,873; the network adds power over a chi-square statistic of the same map when misfit is sparse among many covariates; the map finds a missed interaction that one-covariate diagnostics cannot see; and, applied to a published risk model on new patients, it is an exactly valid test of calibration within patient subgroups, where the calibration belt has little power. In the SUPPORT study of 8,873 inpatients, DeepGOF-1 rejects a linear in-hospital mortality model, its map shows the U-shaped risks of blood pressure and respiratory rate that a calibration curve hides, and it guides the repairs. It ran in 13 seconds; the projection test, the strongest omnibus rival, took 9 hours 53 minutes and 4.5 GB on the same data, too slow for routine use. The test is deepgof1() in the R package ebrahim.gof.

Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.36142v2 Announce Type: replace-cross Abstract: In Bayesian inference problems with non-Gaussian observation noise, the posterior is only as accurate as the noise density, and gradient-based samplers need that density and its gradient evaluable pointwise, whether from an explicit expression or from code, and without an inner solve. We propose Copula Active Subspaces (CAS) to represent this noise density. A componentwise rank transform isolates the noise law's dependence in its copula, and a rank-$r$ reduction keeps only the directions along which that dependence varies. These directions are the leading eigenvectors of the copula score covariance $\boldsymbol{C} := \mathrm{Cov}_{\pi_{\boldsymbol{Z}}}(\nabla\log c^{Z})$, which is what makes the reduction a copula active subspace. Because $\boldsymbol{C}$ vanishes when the coordinates are independent, these are directions of dependence, which the covariance of the data need not identify. From this construction follow a Gaussian-reference KL divergence bound with the explicit constant $\tfrac{1}{2}$, minimized over all rank-$r$ reductions by exactly this eigenspace; a diagnostic for the error the reduction leaves behind, computable from the samples alone; and, from Hermite score matching, a reduced log-density and gradient in closed form, with the truncation orders and the Stage-2 regularization constants chosen on validation samples. The reduction replaces a $d$-dimensional density estimation problem by an $r$-dimensional one. On a $d=20$ noise law and a Bayesian inference problem with that noise, CAS lowers noise KL divergence more than fivefold and posterior KL divergence more than sevenfold against Gaussian-copula, product-of-marginals, and PCA-subspace baselines, and lowers noise KL divergence by factors of about $3.5$ and $2.7$ on two further $d=20$ examples.

Efficient conformal prediction intervals for time series: Online PID-Expert aggregation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02777v1 Announce Type: new Abstract: For a given point forecaster, proportional-integral-derivative (PID) calibration configurations can attain similar overall coverage yet produce different interval widths. We introduce PID-Expert, an online aggregation method for improving the efficiency of conformal prediction intervals for time series. PID-Expert combines thresholds from a fixed library of PID calibrators, each evolving under its own coverage feedback. Aggregation weights depend on normalized interval width and miscoverage, while a shared multiplier adapts the miscoverage penalty using feedback from the reported interval. We establish local regret bounds for weighted expert losses under the realized multiplier sequence and, separately, a pathwise upper bound on time-averaged aggregate miscoverage, with control in expectation and almost surely under a stability condition. Across four simulation settings and two real-data applications, PID-Expert produces narrower mean intervals than a prespecified Conformal PID benchmark while keeping overall empirical coverage close to the nominal level. Compared with expert selection and equal averaging, aggregation generally provides a more balanced coverage--width trade-off across forecasting settings. Rolling analyses further reveal local coverage--efficiency trade-offs, particularly following abrupt distributional shifts. Overall, PID-Expert reduces reliance on a single PID configuration while improving interval efficiency.

Psychometric Tests: Quantifying the Consequences of Low Reliability and Improving Reliability Estimation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03006v1 Announce Type: new Abstract: We introduce a set of consequence-based measures that quantify the misclassification arising from imperfect reliability in multi-item psychometric scales. Particular attention is given to the probability of individuals in extreme latent-trait percentiles being correctly identified from their observed scores. These cost functions provide a principled and interpretable way to characterise how inadequate reliability distorts classification and reduces the informational value of test scores. We also examine methodological issues in estimating reliability under common-factor models, with emphasis on McDonald's omega and the construction of accurate confidence intervals. To address the computational burden of model fitting, especially in small samples, we derive a modified version of Cronbach's alpha that closely approximates omega when the common-factor model holds. This estimator has comparable sampling variability to omega while requiring no parameter estimation, offering a practical and computationally efficient alternative. y

Jumping up and down: Denoiser diffusion models for discrete ordinal data

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02754v1 Announce Type: cross Abstract: Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.

Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03679v1 Announce Type: cross Abstract: The dynamics of cells, organisms, and fluids are often modeled as probability distributions evolving over time. Reconstructing and extrapolating this evolution from unpaired snapshots requires assumptions about the underlying process. Wasserstein gradient flows are a common choice, but they cannot describe conservative or periodic dynamics. Lagrangian mechanics in Wasserstein space covers both, but existing methods for learning it are simulation-based: they run a numerical solver at every training step, which makes training expensive. We propose Double-Stitch, a simulation-free method that learns these mechanics by penalizing the residual of the equation of motion along a learned population path. We derive this equation from a Clebsch variational principle that does not require gradient velocities, and show that the residual vanishes exactly when the equation holds. We test Double-Stitch on synthetic, single-cell and ocean vortex datasets and find that it matches or outperforms gradient-flow methods and simulation-based WLM on most tasks, while training $4$-$14$ times faster than WLM. We provide a JAX implementation of Double-Stitch at https://github.com/BasisResearch/stitching.

Flexible Nonparametric Inference for Causal Effects under the Front-Door Model

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2312.10234v4 Announce Type: replace Abstract: Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-n consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods.

Regularized Exponentially Tilted Empirical Likelihood for Bayesian Inference

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2312.17015v5 Announce Type: replace Abstract: Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood to address this issue. Our method removes the convex hull constraint using a novel regularization technique, incorporating a continuous exponential family distribution to satisfy a Kullback--Leibler divergence criterion. The regularization arises as a limiting procedure where pseudo-data are added to the formulation of exponentially tilted empirical likelihood in a structured fashion. We show that this regularized exponentially tilted empirical likelihood retains certain desirable asymptotic properties with improved finite sample performance. Simulation and data analysis demonstrate that the proposed method provides a suitable pseudo-likelihood for Bayesian inference.

Quantifying and Correcting Measurement Error in LLM-Generated Classifications: A Beta-Binomial Latent Class Model for Correlated Repeated Judgments

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2510.23874v5 Announce Type: replace Abstract: Large language models are increasingly used to classify text at scale. Because their outputs are stochastic, it is common to query a model several times per item and aggregate the results, and latent class models offer a principled way to convert such repeated ratings into estimates of outcome prevalence and of the model's error rates. These models assume that repeated ratings of the same item are conditionally independent given the true label. We examine this assumption using 52,500 judgments from seven open-weight models ranging from 1B to 32B parameters, collected under three prompt conditions with ten samples per item on a public benchmark with human labels. On the balanced split of the benchmark, intraclass correlations lie between 0.50 and 0.93, so ten ratings carry the information of between 1.07 and 1.81 independent ratings. Under this correlation, a latent class model with a binomial likelihood is both miscalibrated and biased. Its nominal 95% intervals for the false acceptance rate contained the value computed from human labels in none of 42 settings, and it underestimated the total error rate in all 42. We propose a beta-binomial latent class model with a single correlation parameter, establish its identifiability and that of extensions to covariates, treatment effects and partially labeled data, and show that on the balanced split it raises the coverage of nominal 95% intervals for the prevalence and the false acceptance rate to 0.90. Recovery of the latent state is governed by the gap between the model's acceptance rates on truly positive and truly negative items, which equals Youden's J and predicts recovery almost monotonically (Spearman correlation 0.96). When this gap is small, a labeled subset improves estimates of prevalence but not the classification of individual items. Simulation studies designed around the identification conditions support these findings.

Empirical Bayes Method for Large-Scale Multiple Testing with Heteroscedastic Errors

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2512.24611v2 Announce Type: replace Abstract: In this paper, we address the normal mean inference problem, which involves testing multiple means of normal random variables with heteroscedastic variances. Most existing empirical Bayes methods for this setting are developed under restrictive assumptions, such as the scaled inverse-chi-squared prior for variances and unimodality for the non-null mean distribution. However, when either of these assumptions is violated, these methods often fail to control the false discovery rate (FDR) at the target level or suffer from a substantial loss of power. To overcome these limitations, we propose a new empirical Bayes method, gg-Mix, which assumes only independence between the normal means and variances, without imposing any structural restrictions on their distributions. We thoroughly evaluate the FDR control and power of gg-Mix through extensive numerical studies and demonstrate its superior performance compared to existing methods. Finally, we apply gg-Mix to three real data examples to further illustrate the practical advantages of our approach.

Scalable and Robust Spatial Prediction via Multi-Resolution Ensembles of Predictive Processes

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2603.19977v2 Announce Type: replace Abstract: Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate this burden by projecting the original process onto a reduced set of $m\ll n$ inducing points. However, existing theory requires $m$ to grow with $n$, creating a trade-off between accuracy and computational efficiency. We address this challenge by introducing an ensemble of PPs based on spatial partitioning, and propose a novel partitioning and patching scheme with desirable properties. By generalizing the convergence results of PPs, it becomes possible to explicitly balance scalability and accuracy: increasing the number of ensemble components slows down the convergence but substantially improves computational efficiency. We further show theoretically that, despite the limited approximation accuracy of PPs with fixed, small $m$, they provide predictions that are more robust to training data contamination. Motivated by these findings, we finally introduce a multi-resolution ensemble that combines ensembles over possibly overlapping coarse to fine partitions. Unlike previous multi-resolution approaches, our method targets predictive robustness rather than accurate covariance approximation. Simulations and large-scale geostatistical applications demonstrate that our approach delivers accurate, robust predictions while being computationally efficient, thereby providing a practical and broadly applicable solution for spatial prediction.

Bayesian Univariate-Guided Sparse Regression for Ultra-High-Dimensional Data

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2604.04964v3 Announce Type: replace Abstract: Ultra-high-dimensional genomic studies require simultaneous identification of sparse signals, control of spurious discoveries, and computationally feasible inference when the number of predictors can reach hundreds of thousands or more. We propose Bayesian Univariate-Guided Sparse Regression (BUGS), a global--local shrinkage framework that incorporates marginal association information directly into the prior through continuous modulation of shrinkage. By embedding univariate guidance within the nonlinear variance structure of a regularized horseshoe prior, BUGS adaptively differentiates predictors with strong and weak marginal evidence without relying on hard screening. We establish theoretical results on prior concentration, posterior contraction, and guidance-induced shrinkage separation, and characterize the behavior of the prior under uninformative guidance. For ultra-high-dimensional problems, we develop BUGS-Active, an active-set MCMC approximation that reduces the cost of local-scale updates from $O(p)$ to $O(|A_n|)$ while retaining global coefficient updates. Simulations under independent and correlated designs show strong signal recovery and substantially lower empirical false discovery rates relative to competing methods. We apply BUGS-Active to a DNA methylation study of developmental age with $n=1051$ samples and approximately $850{,}000$ CpG sites, jointly analyzing all probes without pre-screening. The analysis yields strong out-of-sample prediction and a sparse set of age-associated CpG sites with stable posterior support. These results illustrate the practical value of marginally guided Bayesian shrinkage for large-scale genomic regression.

Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2605.01157v3 Announce Type: replace Abstract: We develop a coarse-to-fine generalized linear mixed model (CF-GLMM) for scalable spatial prediction of exponential-family responses. CF-GLMM extends coarse-to-fine spatial modeling (CFSM) beyond Gaussian data by sequentially increasing spatial resolution while validation deviance improves, so the terminal resolution need not be specified in advance. The latent spatial process is constructed by aggregating local models, avoiding costly operations on large spatial covariance matrices. An idealized convolution representation links the covariance of our assumed spatial process to a sum of Matern covariances with different ranges. Monte Carlo experiments show that CF-GLMM achieves predictive accuracy comparable to widely used scalable spatial GLMMs while requiring less computation and memory. Its scale-specific components also support exploratory multiscale analysis. An application to COVID-19 infection data in Tokyo illustrates fine-resolution spatial prediction and multiscale characterization of geographical variation. The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).

Uncertainty-Aware Ideal Point Estimation via Variational EM with P\'{o}lya-Gamma identity

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2605.19591v2 Announce Type: replace Abstract: Roll-call data analysis aims to estimate legislators' ideal points and quantify the associated uncertainty. Existing approaches either rely on Bayesian methods implemented via Markov chain Monte Carlo sampling or focus primarily on point estimation, with uncertainty typically assessed through resampling procedures such as the bootstrap. Consequently, the computational burden of these approaches can become substantial when applied to large roll-call datasets. To address this challenge, we propose a computationally efficient likelihood method for estimating ideal points and their standard errors. Leveraging the P\'{o}lya-Gamma identity, we develop a variational expectation--maximization algorithm for estimating ideal points and introduce a variational Louis' method to approximate the observed Fisher information for standard error estimation. Numerical studies and applications to U.S. congressional roll-call data demonstrate that the proposed method produces accurate ideal point estimates and reliable standard errors while being substantially more computationally efficient than existing approaches.

Detection coherence of tests

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2608.11177v2 Announce Type: replace Abstract: There exist tests calibrated under a null narrower than the one implied by their test statistic -- the detection-null set. The part of the detection-null set not in the null is the test's blind spot. A framework for assessing detection coherence -- whether a test's blind spot is empty -- is introduced, built on new concepts of calibration statistic, detector, detection functional, detection-null set, and blind spot. It is demonstrated that the Wilcoxon--Mann--Whitney, Kruskal--Wallis, Friedman, and logrank tests are detection incoherent as unrestricted tests. Detection incoherent tests may become coherent under restrictions that make the blind spot empty, though domain restriction is not a reliable route to coherence in practice, since the boundary of the coherence-restoring domain is unknown and unverifiable. The Kolmogorov--Smirnov and Zaremba tests, and the Maximum Mean Discrepancy test with a characteristic kernel, are shown to be universally detection coherent. Due to the blind spot, a detection incoherent test misses discoveries when non-rejecting and yields spurious discoveries when rejecting, in both cases regardless of sample size. Detection incoherent tests should be abandoned.

Risk-Calibrated Balancing for High-Dimensional Causal Extrapolation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2609.34482v2 Announce Type: replace Abstract: In observational causal inference, covariate balancing is widely used to reduce source-target covariate shift, but under weak overlap in high dimensions, stronger balance can induce concentrated weights and increase variance. Balance measures how well the target covariate distribution is represented, but does not by itself determine how reliably the counterfactual mean can be estimated. We develop risk-calibrated balancing for the average treatment effect on the treated, which applies ridge augmentation to any normalised base weights and selects its penalty using conditional prediction risk of the counterfactual mean. Under a random-effects predictive model, we derive an exact finite-sample decomposition of this risk into residual covariate imbalance and weight-induced variance. For design-independent base weights under proportional asymptotics, we characterise how limiting risk depends on source and target covariance geometry, population mean shift, and weight concentration. For covariate-adaptive base weights, we develop a uniformly consistent target-aware risk estimator whose minimiser attains vanishing scaled oracle excess risk. Simulations show that the high-dimensional risk predictions remain informative for adaptive balancing and that target-aware tuning generally reduces excess target risk. Empirical analyses of job-training and single-cell perturbation data show that risk-calibrated balancing generally improves on the corresponding base estimators, with larger gains under weaker overlap.

Learning Style, Forgetting Semantics: A Case Study of SFT and RFT on Classification Tasks

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02437v1 Announce Type: new Abstract: Why does supervised fine-tuning (SFT) lead to more forgetting than reinforcement fine-tuning (RFT), even when all teacher demonstrations are semantically correct? We study this question on classification tasks where tokens within each semantic class express the same semantic answer in different styles. The tasks share an underlying semantic rule but differ in their prompt distributions and teachers' stylistic preferences. Using a tractable linear-softmax policy, we derive an exact decomposition of the updates into semantic and style components. We show that, at a common policy and prompt, SFT and RFT have parallel semantic updates but differ in their style dynamics. Starting from a policy with no within-class style preference, RFT with exact policy gradients preserves this symmetry, whereas SFT with a nonuniform teacher develops off-axis style drift along a nonzero task mean under population updates. We use this drift to establish a separation under explicit conditions: for population updates from a common perfectly fitted checkpoint, SFT forgetting admits a strictly positive lower bound over a finite training interval, while RFT retains zero semantic error. Simulations over task sequences support these theoretical predictions.

ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02538v1 Announce Type: new Abstract: Inference-time control steers a pretrained generative model towards a target distribution without retraining. We study tilted targets $\pi_0\propto G_0\,p_0$, where $p_0$ is the sampler output distribution and $G_0$ is an evaluable reweighting function. Existing approaches rely on sequential annealing with sequential Monte Carlo (SMC) or parallel annealing with replica exchange (RE). Sequential control is exact but needs large particle populations, whereas no exact parallel control method exists: existing RE corrections approximate an intractable time reversal and are biased. We propose Exact Non-equilibrium COntrol with Replica Exchange (ENCORE), the first exact parallel control method. Each replica stores its generation trajectory, so the upward move is a truncation and the intractable time reversal is never simulated. We prove target invariance and show that the resulting dynamics are those of non-equilibrium replica exchange with the exact time reversal as forward proposal. Under regularity conditions, our diffusion analysis shows that both sequential and parallel control become unstable under refinement of the time discretisation without guidance, whereas guided proposals remain stable and yield diagnostics for tuning the schedule and the computational budget. Across synthetic targets, Boltzmann sampling of biomolecules, and image generation, ENCORE achieves competitive accuracy and diversity, remains robust to sampler perturbations, and applies to distilled samplers where existing RE corrections are unavailable.

High-Dimensional Asymptotics and Dataset Selection for Private Transfer Learning

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02578v1 Announce Type: new Abstract: To commit to buying external data or participate in collaborative learning, one must decide whether the additional data will improve prediction enough to justify the cost. This comes with several challenges: (i) the decision often relies only on aggregated statistics available publicly, rather than individual-level data; (ii) covariate and model shifts can induce negative transfer, so the additional data deteriorates rather than improves performance; (iii) if the data is sensitive, its privatization requires the injection of noise, which can also offset the benefit of a larger sample size. In this paper, we model the problem of dataset selection through high-dimensional regression with multiple heterogeneous sources and a weighted ridge estimator. Our approach uses only summary statistics and it gives privacy guarantees either on labels only or jointly on features and labels, in terms of $\rho$-zero-concentrated differential privacy. The main technical contribution is a deterministic equivalent of the test error, which captures the interactions between sample size, covariance structure, model shift, regularization and privacy noise. Our theory allows to optimize hyperparameters (weights and ridge regularizers) and, more broadly, to decide when private external datasets are useful without accessing the data itself but only relying on population-level quantities. This provides a theoretically tractable foundation for private transfer learning, which we support via experiments on both synthetic and real-world datasets.

Hold-Out Scoring for Efficient Gaussian DAG Learning

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02785v1 Announce Type: new Abstract: High-dimensional Gaussian DAG learning faces a statistical-computational gap: methods with sharp sample complexity rely on computationally expensive subset search and a supplied indegree bound, whereas polynomial-time alternatives have less favorable sample complexity. We introduce HOST, an efficient DAG learning algorithm that replaces subset search with nodewise hold-out scoring and convex regression, without requiring a supplied indegree bound. Our key insight is that recovering a correct ordering does not require uniformly small estimation errors in ordering scores but only one-sided control of those errors. In the ordering step, HOST exploits the fact that score estimation using hold-out samples inflates ordering scores in expectation, which is the favorable direction for candidates that should not yet be selected. Given the ordering, HOST recovers parents by recursively removing indirect effects from total effects between two nodes. Under suitable conditions, HOST exactly recovers a $p$-node DAG of maximum indegree $d$ with sample complexity of order $d\log p$ in polynomial time. Experiments show that HOST achieves competitive graph recovery while exhibiting favorable runtime scaling.

Invariance of Clustering Operations in Causal Effect Identification

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03101v1 Announce Type: new Abstract: Clustering variables in causal graphs reduces the size of the graph and simplifies causal inference. However, arbitrary clustering can alter crucial causal relations among variables and lead to erroneous conclusions. While the identifiability of a causal effect in the clustered graph implies the identifiability in the original graph under mild conditions, nonidentifiability in clustered graph does not imply nonidentifiability in the original graph without further assumptions. When both identifiability and nonidentifiability are preserved, the clustering operation is called identification invariant. We present a broad class of clustering operations that are identification invariant based on conditions related to the c-components of the original graph. Finally, we demonstrate use of the results in practical settings.

Predictively Oriented Gaussian Process Posteriors

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03201v1 Announce Type: new Abstract: Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitioners to make a number of design decisions, such as the choice of the kernel and the observation model. Suboptimal choices can produce misspecified models that do not capture the underlying data generating process. We introduce Predictively Oriented Gaussian Processes (PrO-GPs), which treat predictive uncertainty as the primary inferential target and provide a robust alternative to standard GPs. Although direct computation of a PrO posterior for nonparametric models is intractable, we derive a reduced formulation and practical sampling scheme for efficient computation. Through synthetic and real data experiments, we show that PrO-GPs produce better calibrated predictive distributions under model misspecification compared to standard GP approaches.

Iterating Consistency Models: Stability, Error Bounds and Noise Schedules

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03414v1 Announce Type: new Abstract: Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that are highly sensitive to the schedule and that existing theory does not fully explain. To provide accuracy guarantees and guide CM sampler design, we analyze multistep CM sampling as a composition of noising and approximate denoising operators. Under explicit, verifiable stability assumptions, we derive a non-asymptotic error bound that separates contraction of the initialization error from accumulation of approximation error. The bound assigns distinct roles to the schedule: large early noise levels drive contraction, while small late noise levels control the residual bias. As a corollary, we obtain explicit constants for strongly log-concave and semi-log-concave targets. We further establish a complementary guarantee whose assumptions, one-step accuracy and stability, can be estimated for a given trained model. Experiments show that the contraction and approximation profiles entering our bounds can be reliably measured and closely match the predicted functional forms. Together, these results provide a meaningful convergence theory for multi-step CMs and a practical route to sampler design.

When Is Accuracy Evidence? A Unified Theory of Generalisation, Validation, and Information Fusion

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03465v1 Announce Type: new Abstract: K-fold cross-validation (CV) is widely used as evidence of out-of-sample performance, although folds are neither independent experiments nor equally informative under heterogeneous data. Cross Upper-Bound Validation (CUBV) replaces point-wise CV accuracy by conservative upper bounds on true risk. Here we generalise CUBV through a single exponential framework in which the moment-generating function of the generalisation gap is controlled by a cumulant envelope gamma(lambda). This yields a family of risk bounds covering Hoeffding-, Bernstein-, dependency-aware, PAC-Bayesian, and heterogeneous source-fusion settings. For K-fold CV, dependence between fold-wise gaps is modelled through a joint sub-Gaussian proxy matrix. Under equicorrelation, this gives an effective number of folds, Keff = K/[1+(K-1)rho], showing that increasing K does not necessarily increase statistical evidence when folds are strongly dependent. The framework is also extended to posterior distributions over predictors and weighted multi-source fusion, where weights are selected by minimising an upper bound on future risk rather than empirical error alone. Experiments with trained linear classifiers on heterogeneous multimodal Gaussian mixtures compare K-fold CV with full-sample resubstitution plus risk correction. Bounds are evaluated by coverage and tightness. In low-dimensional small-sample settings, K-fold partitioning can increase uncertainty because individual folds under-represent minority modes, while corrected resubstitution can remain valid and tighter; this effect disappears as sample size increases. Overall, gamma-CUBV separates observed performance, uncertainty, dependence, model complexity, and confidence into explicit terms, providing a unified route from CV scores to risk statements and a principled validation criterion for heterogeneous small-sample applications such as neuroimaging.

AREX: Affine-Residual Exponential Integrator for Few-Step Sampling in Flow Matching

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03483v1 Announce Type: new Abstract: We introduce AREX, a training-free sampler for pretrained flow matching models that uses the target mean and covariance to capture an analytically tractable part of the sampling dynamics. We show that the velocity field of the moment-matched Gaussian target is the $L^2$-optimal affine approximation to the marginal velocity field. This motivates decomposition of the learned dynamics into an affine component over the whole sampling path, determined by the first two target moments, and a neural residual term. AREX keeps the affine component and integrates it using an explicit matrix-valued propagator. In turn, we only require to integrate over the residual term. This differs from scalar exponential integrators, which analytically handle only isotropic linear dynamics. Across image and text-to-image generation tasks, AREX consistently improves sample fidelity in the few-step sampling regime without retraining the underlying model.

Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03647v1 Announce Type: new Abstract: Many machine learning methods aim to approximate the lower-dimensional manifold on which the data lives. A desirable feature of such methods is that they should capture the epistemic uncertainty of this learned manifold. One model that achieves this is the Gaussian Process Latent Variable Model, in which a Gaussian Process (GP) mapping from the latent space provides an estimate of the uncertainty of the manifold. However, the effectiveness of this uncertainty estimation is limited by the mean-field variational approximation between the GP inducing points and the latent variables. In this work, we apply Amortized Structured Stochastic Variational Inference to allow the variational posterior for the latent space to be conditionally dependent on the value of the inducing points. We demonstrate that this more flexible variational posterior improves several metrics relating to the reconstruction of points on the data manifold.

Feature tracking in physics-informed neural networks via joint optimization of nonlinear deformation manifolds: application to shocks

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02230v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.

Nearest-neighbour baselines for fingerprint prediction from MS/MS spectra under different assumptions

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02249v1 Announce Type: cross Abstract: It has recently been shown that nearest-neighbour retrieval provides a strong baseline for molecular fingerprint prediction from MS/MS spectra, with several variants matching or outperforming current deep learning models (Khoo and Barzilay, 2026; Liu et al., 2026; Gupta et al., 2026). Importantly, "nearest neighbour" encompasses a family of retrieval methods that differ in the information assumed to be available at inference. In this report, we systematically compare several nearest-neighbour variants and show how these differing assumptions affect performance. Our goal is to establish stricter baselines that enable more rigorous benchmarking and better measure progress in this area.

Counterfactual Predictions in Scientific Emulators Without Controlled Experiments

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02252v1 Announce Type: cross Abstract: Many scientific questions require reasoning about what was never observed: What if the conditions, interventions, or history had been different? Models can predict accurately on observed data yet fail on such what-if queries when correlated inputs are varied independently. A common remedy is to add controlled simulation data in which these factors are explicitly disentangled, but this requires access to a simulator, can be computationally expensive, and inherits the simulator's modeling assumptions. We introduce ReRoute, a framework for targeted scientific what-if prediction that combines factual data with partial mechanistic knowledge, without requiring controlled intervention data for adaptation. ReRoute fixes the queried input of a pretrained backbone to a reference value, reintroduces its variation through a known mechanistic pathway, and fine-tunes on the original factual data, while leaving downstream effects to the learned dynamics. We provide a causal identification result for this construction under explicit structural assumptions, with the core argument machine-checked in Lean. After showing that ReRoute achieves highly accurate counterfactual predictions in a controlled advection-diffusion system where exact responses are available, we turn to state-of-the-art climate emulation. On held-out coupled-climate interventions, ReRoute reduces aggregate climate error by 18.2-31.8% under severe CO$_2$ distribution shifts while preserving skill under standard conditions, at a small fraction of the cost of retraining on additional controlled simulations, without even accounting for the substantial expense of generating such data. Finally, on an emulator trained from historical ERA5 reanalysis, where no counterfactual reference exists, ReRoute preserves substantially more of the surface warming implied by the observed boundary conditions under a fixed-CO$_2$ counterfactual.

TRACE: A Reproducible Benchmark for Electricity Price Forecasting with Official Operational Text

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02256v1 Announce Type: cross Abstract: Electricity price forecasting (EPF) supports scheduling, bidding, and risk management in electricity markets, yet existing benchmarks focus mainly on numerical inputs, leaving the forecasting value of forecast-time textual context insufficiently evaluated. We introduce TRACE, a reproducible benchmark of 7,300 zone--day instances pairing prices from five zones in a major U.S. market with official operational text available at the forecast cutoff. TRACE reconstructs official operational text at each cutoff, preventing post-cutoff information leakage. We evaluate TRACE for semantic alignment and forecasting value. Semantic assessments align with central movement and both tail risks in ground-truth prices, most consistently for upper-tail price risk. Forecasting value is reflected in a median 7.4\% reduction in upper-tail pinball loss across time-series foundation models. A controlled cross-day text-mismatch ablation reverses the gains, falling below the no-text baseline.

Differential Privacy of Gradient Descent on Perturbed Objectives

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02716v1 Announce Type: cross Abstract: Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer. We study the finite computation obtained by releasing the $N$-th iterate of deterministic gradient descent on $w\mapsto F(w;S)+\langle z,w\rangle$, where $z\sim\mathcal N(0,\sigma^2I_d)$ is drawn once before optimization. For strongly convex and smooth objectives with Lipschitz Hessian, we prove an explicit condition under which the map $z\mapsto w_N$ is a $C^1$-diffeomorphism on the bounded domains used in the privacy argument, with a quantitative lower bound on the smallest singular value of its Jacobian. This permits a direct change-of-variables analysis of the finite iterate. For generalized linear models, the resulting privacy-profile bound has no explicit ambient-dimension factor once the iteration condition holds, and its finite-iteration correction decreases geometrically. By letting the free truncation parameter grow slowly with $N$, we recover the corresponding exact-minimizer certificate in the limit. We also bound the expected excess empirical risk by $d\sigma^2/(2\mu)$ plus a geometrically decreasing optimization term, and transfer the result to population risk without an additional multiplicative condition-number factor in the leading statistical terms.

Nearly Optimal Fixed-Confidence Best-Arm Identification with 1-Bit Feedback

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02771v1 Announce Type: cross Abstract: We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set, and receives only a single bit indicating whether the sampled reward belongs to that set. We consider a distribution-free finite-variance setting with arm-wise localization, where direct empirical mean estimation is no longer available and clipping becomes unavoidable. We first formulate a time-uniform 1-bit mean-estimation primitive based on randomized threshold queries and a clipped tail-integral identity. We then embed this primitive into candidate-challenger best-arm identification algorithms. A fixed-clipping algorithm gives a simple anytime $(\epsilon,\delta)$-PAC guarantee, while a phased adaptive-clipping algorithm matches the clipping level to the current resolution and yields a gap-adaptive sample complexity. We also prove a $K$-arm worst-case information-theoretic lower bound showing that the logarithmic penalty caused by finite-variance 1-bit feedback is intrinsic. This bound matches the leading dependence of the phased algorithm up to lower-order $\log\log$ factors.

Muon Learns Facts Better: Understanding the Role of Spectral Orthogonalization

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02798v1 Announce Type: cross Abstract: The Muon optimizer applies spectral orthogonalization to matrix-valued updates and has shown strong performance in large-scale neural network training, yet the mechanisms of this transformation in feature learning remain poorly understood. In this work, we investigate this question through a tractable factual-recall model, where a fact maps each subject-relation pair to an answer, and a linear transformer learns the subject- and relation-dependent information required to recover this mapping. The transformer is optimized with gradient flow (GF), spectral GF, or Sign GF, which are continuous-time limits of gradient descent, Muon, and Adam, respectively. Prior studies (Nichani et al., 2025) have shown that when the number of subjects exceeds the number of relations, GF learns relation-dependent information before subject-dependent information, producing a feature-separation phase during training. We characterize this separation with the learning times when the subject- and relation-dependent components of the prediction reach a target accuracy. With $S$ subjects and $R$ relations, GF has a learning-time ratio of $\widetilde{\Theta}(\sqrt{S/R})$, whereas Spectral GF reduces this ratio to $\widetilde{\Theta}(1)$. In addition, for fixed $S$ and $R$, the subject- and relation-dependent errors decay as $1/(T\log T)$ in training time $T$ under GF, but as $\exp(-\mathrm{poly}(T))$ under spectral GF. Finally, we show that GF and spectral GF are equivariant under orthogonal transformations of the token embeddings, whereas Sign GF is not: Different orthonormal embeddings can potentially produce no feature separation, a large feature-separation phase, or even a reversed learning order. These results provide a mechanistic view of how spectral orthogonalization can fundamentally reshape feature-learning dynamics.

Below what training size do deep tabular generators stop beating trivial baselines? A preregistered benchmark on a size ladder of clinical and standard datasets

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03500v1 Announce Type: cross Abstract: Deep tabular generative models are benchmarked on datasets with tens of thousands of rows; clinical datasets have hundreds. We preregistered and ran a size-ladder benchmark to find where the two regimes diverge: 8 public datasets subsampled from 200 to 20,000 training rows, seven generators (independent marginals, Gaussian copula, SMOTE, unconditional SMOTE, CTGAN, TVAE, TabDDPM) with a fixed 20-trial tuning budget and 5 evaluation seeds, plus 4 natively small clinical datasets at true size, for 2,220 committed runs in total. The primary metric is the AUROC of fixed classifiers trained on synthetic and tested on real data. In 23 of 24 (dataset, deep model) pairs no deep model ever beats the best trivial baseline by more than seed noise, at any training size we measured. The best baseline wins 40 of 49 (dataset, size) cells. Our preregistered prediction that the deep models' ranking would be unstable at small sizes is falsified: mean Kendall tau between adjacent rungs below 5,000 rows is 0.806, above our 0.8 threshold, and stability is highest at the smallest sizes rather than lowest. One caveat bounds all of this: in 81% of cells the gap between the top two methods is smaller than the variation between seeds. Finally, method rankings on natively small clinical datasets agree only moderately with rankings on subsampled large ones (mean tau 0.57 to 0.64), which questions whether a subsampled large dataset can stand in for a small one. All 2,220 result files, the preregistration and its hash, and the code that regenerates every figure and number from those files are public.

Broken scale symmetries in undercomplete linear autoencoders

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03640v1 Announce Type: cross Abstract: Neural network loss landscapes have many symmetries, which are preserved by gradient flow but broken by finite-stepsize stochastic gradient descent (SGD). A canonical example of such a symmetry is scale in homogeneous networks: one can scale up the parameters in one layer and down in the next without changing the network output. Previous work has documented cases in which SGD breaks this symmetry in favor of balancing gradient noise or minimizing fluctuations. Here, we show that the solution geometry of undercomplete linear autoencoders instead selects a preferred sign for scale drift: on the PCA solution manifold, SGD favors large decoder weights. This directed scale drift occurs on a slow timescale, and its dynamics admit an analytically-tractable effective description. However, it cannot continue indefinitely: increasing scale eventually drives the dynamics towards a finite-stepsize stability boundary. The resulting solutions are sharper than a balanced baseline in the sense of the maximum eigenvalue of the loss Hessian, but different sharpness measures can move in opposing directions. Thus, undercomplete autoencoders give a concrete illustration of how loss geometry can convert residual gradient noise into directed motion along a manifold of functionally-equivalent solutions.

When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03646v1 Announce Type: cross Abstract: Stationarity rewards memory, but after a change the same history can mislead. We ask when forgetting should be permitted. E-process-authorized Thompson sampling (e-ATS) gives each arm full-history and discounted Beta states. An anytime-valid e-process first authorizes the discounted state, then a reversible relevance score controls its influence. Before authorization, e-ATS exactly follows optimistic Thompson sampling (OTS). Under a Beta-Bernoulli prior-predictive stationary model, e-ATS's probability of ever departing from OTS is at most the chosen $\alpha_E$, without fitted thresholds. Relative to e-ATS, removing authorization increased mean normalized dynamic pseudo-regret by $38.4\%$ on the registered suite but reduced it by $7.5\%$ on the literature-derived replay suite. Therefore, evidence controls when adaptation begins, not whether it always helps.

Estimating axial symmetry using random projections

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2512.21417v2 Announce Type: replace Abstract: We study the directions of axial symmetry of multivariate distributions and relate the measure or cardinality of this set to spherical symmetry. Under Carleman's condition, two independent random projections identify all true axes of symmetry in $\RR^2$ almost surely. We propose a level-set estimator of the symmetry axes and prove its Hausdorff consistency, in arbitrary dimension, for the zero set of the population criterion based on finitely many projections. Together with planar identification, this gives a consistent estimation of the true axes of symmetry in dimension two.

Level sets and maximum likelihood estimation for the Ising model

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2511.20925v2 Announce Type: replace Abstract: Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows one to apply the problem to the Ising model from statistical mechanics. We propose a full characterization of the existence of the MLE for the Ising model among the level sets used in related combinatorial problems. We then establish new bounds for the size of the smallest set of uniqueness for the products of Rademacher functions.

High-Dimensional Asymptotics of Differentially Private PCA

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2511.07270v4 Announce Type: replace Abstract: In differential privacy, random noise is introduced to privatize summary statistics of a sensitive dataset before releasing them. The noise level determines the privacy loss, which quantifies how easily an adversary can detect a target individual's presence in the dataset using the published statistic. Most privacy analyses provide non-asymptotic upper bounds on the privacy loss which hold uniformly across all datasets. Sometimes, these bounds can be pessimistic on a given dataset. In such cases, it can be useful to complement these privacy bounds with sharp privacy characterizations that quantify a mechanism's exact privacy loss on a given dataset. With this goal, we study differentially private principal component analysis (PCA), where the goal is to privatize the leading principal components of a dataset with $n$ samples and $p$ features. We analyze the exponential mechanism and provide sharp asymptotic characterizations of its utility and privacy loss in the high-dimensional limit ($p \rightarrow \infty$). We show that in this limit, detecting a target individual's presence using privatized principal components is asymptotically equivalent to distinguishing between two Gaussians with different means, where the mean difference depends on certain spectral properties of the dataset. Our analysis combines the hypothesis-testing formulation of privacy guarantees proposed by Dong, Roth, and Su (2022) with Le Cam's contiguity arguments.

Factorization by extremal privacy mechanisms: new insights into efficiency

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2507.21769v2 Announce Type: replace Abstract: We study the problem of efficiency under $\alpha$ local differential privacy ($\alpha$ LDP) in both discrete and continuous settings. Building on a factorization lemma, which shows that any privacy mechanism can be decomposed into an extremal mechanism followed by additional randomization, we reduce the Fisher information maximization problem to a search over extremal mechanisms. The representation of extremal mechanisms requires working in infinite dimensional spaces and invokes advanced tools from convex and functional analysis, such as Choquet's theorem. Our analysis establishes matching upper and lower bounds on the Fisher information in the high privacy regime ($\alpha \to 0$), and proves that the maximization problem always admits a solution for any $\alpha$. As a concrete application, we consider the problem of estimating the parameter of a uniform distribution on $[0, \theta]$ under $\alpha$ LDP. Guided by our theoretical findings, we design an extremal mechanism that yields a consistent and asymptotically efficient estimator in high privacy regime. Numerical experiments confirm our theoretical results.

Compatibility and Exclusivity of Loss Functions under Statistical Optimality

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2507.12447v5 Announce Type: replace Abstract: In applications a loss is usually chosen from a family, like a quantile level, a robustness threshold or a surrogate margin loss. In this paper, we ask which of these choices change the optimal decision. A model, a class of decision rules and an optimality criterion define an optimality map $L\mapsto\cO(L)$. Two losses are compatible when they share an optimal rule, and exclusivity regions are unions of the connected components of this relation. When $\cO$ is single-valued these components are the fibres of the map, and the problem is to identify the statistically meaningful features of a loss that determine its fibre. Under explicit model assumptions, the answer is the quantile level for generalized piecewise linear quantile scores and the margin invariant (equivalently, the link) for regular margin losses read at the score level. For canonical Huber losses on strictly skewed location models, a class that includes every asymmetric Laplace model, it is the threshold. Two structural results hold in general. Convex interpolation between losses with distinct unique Bayes acts meets uncountably many compatibility classes, so the structure is conic rather than convex. Coarsening the optimality operator can only merge components, which is how the known common Bayes classifier of calibrated surrogates arises.

Asymptotically distribution-free goodness-of-fit testing for point processes

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2503.24197v3 Announce Type: replace Abstract: Consider an observed path from a multivariate temporal point process $N$ with law $\mathbb P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathbb P$ belongs to a given parametric family, we construct a compensated empirical process to which we apply a suitable innovation martingale transformation. We prove that the resulting test process converges weakly to a standard Wiener process. Consequently, taking a testing functional of this process yields an asymptotically distribution-free goodness-of-fit test for parametric point processes. Furthermore, for standard test statistics based on the increments of this test process, we establish consistency under alternative hypotheses. We assess the performance of the proposed testing procedure through a Monte Carlo simulation study and illustrate its practical utility with two real-data examples.

Tracy-Widom, Gaussian, and Bootstrap: Approximations for Leading Eigenvalues in High-Dimensional PCA

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2503.23097v2 Announce Type: replace Abstract: Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has fluctuations of order $n^{-2/3}$ that can be approximated by a Tracy-Widom distribution, while in the supercritical regime, it has fluctuations of order $n^{-1/2}$ that can be approximated with a Gaussian distribution. However, the statistical problem of determining which regime underlies a given dataset is far from resolved. We develop a new testing framework and procedure to address this problem. In particular, we demonstrate that the procedure has an asymptotically controlled level, and that it is power consistent for certain alternatives. Also, this testing procedure enables the design a new bootstrap method for approximating the distributions of functionals of the leading sample eigenvalues within the subcritical regime -- which is the first such method that is supported by theoretical guarantees.

Estimation of conditional inequality curves and measures via estimating the conditional quantile function

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2412.20228v4 Announce Type: replace Abstract: In the paper conditional inequality curves and measures are proposed which allow us to describe the inequality/concentration of the conditional distribution of the feature we are interested in with respect to certain continuous variables. Moreover, for a graphical illustration of the change in values of the proposed conditional indices, a curve of conditional inequality measures is introduced. To estimate the curves and measures, a new method is proposed to estimate the conditional quantile function. This method uses quantile regression estimates for a given set of quantile orders, followed by isotonic regression on the estimated regression coefficients to ensure that the estimated conditional quantile function is nondecreasing. The consistency of the proposed estimators is proved while their finite sample performance is evaluated through simulation studies and compared with existing approaches. Finally, practical application of conditional curves and measures is demonstrated by determining estimated curves of conditional salary inequalities with respect to years of experience in different employee tenure groups, based on some real data. The code used to prepare the simulation results presented in this paper is available in a dedicated GitHub repository.

KL Convergence Guarantees for Score diffusion models under minimal data assumptions

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2308.12240v3 Announce Type: replace Abstract: Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then harnessed to simulate the corresponding time-reversal process, ultimately enabling the generation of approximate data samples. Despite their evident practical significance these models carry, a notable challenge persists in the form of a lack of comprehensive quantitative results, especially in scenarios involving non-regular scores and estimators. In almost all reported bounds in Kullback Leibler (KL) divergence, it is assumed that either the score function or its approximation is Lipschitz uniformly in time. However, this condition is very restrictive in practice or appears to be difficult to establish. To circumvent this issue, previous works mainly focused on establishing convergence bounds in KL for an early stopped version of the diffusion model and a smoothed version of the data distribution, or assuming that the data distribution is supported on a compact manifold. These explorations have led to interesting bounds in either Wasserstein or Fortet-Mourier metrics. However, the question remains about the relevance of such early-stopping procedure or compactness conditions. In particular, if there exist a natural and mild condition ensuring explicit and sharp convergence bounds in KL. In this article, we tackle the aforementioned limitations by focusing on score diffusion models with fixed step size stemming from the Ornstein-Uhlenbeck semigroup and its kinetic counterpart. Our study provides a rigorous analysis, yielding simple, improved and sharp convergence bounds in KL applicable to any data distribution with finite Fisher information with respect to the standard Gaussian distribution.

Does a mortality schedule need a Makeham term? Calibrating the likelihood-ratio test

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03685v1 Announce Type: cross Abstract: Whether a fitted mortality model needs a Makeham term, the non-negative constant representing background mortality, is commonly decided with a likelihood-ratio test. Because the constant cannot be negative, testing its absence places the parameter on the boundary of its range, and the usual chi-squared calibration does not apply. Assuming independent Poisson death counts and standard regularity conditions, we show that when the constant is the only parameter on a boundary the statistic converges to an equal mixture of a point mass at zero and a chi-squared distribution with one degree of freedom, so that at the 5% level the critical value is 2.71 rather than 3.84. We give conditions under which the correction holds for Makeham models, verify them for Gompertz-Makeham and gamma-Gompertz-Makeham, and quantify the information the data carry about the constant, which fixes the local power of the test, the smallest term it can detect, and how fast detectability falls as the age window narrows. When a gamma-frailty variance is estimated and its true value is also zero, the limit is no longer a chi-squared mixture and the usual correction rejects too often. Monte Carlo experiments show that the conventional cutoff rejects at half the nominal level, that a correctly calibrated test can still miss a term at its own detection threshold in most samples, and that excess rejections under an estimated zero frailty variance persist as exposure grows.

Cross-Fitting Under Nonregularity: Normality and Inference via Locality

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02944v1 Announce Type: cross Abstract: Cross-fitting is routine in much of applied research. While conventional confidence intervals that ignore cross-fold dependence are asymptotically valid in several settings, they undercover in many applications that share a common form of nonregularity: from the classic cross-validation problem of testing whether a fitted model outperforms another, to testing for heterogeneous treatment effects with machine learning, to estimating the value of a potentially non-unique optimal treatment regime. Exploiting a new locality condition, I show that a large class of cross-fitting estimators still satisfies a central limit theorem despite the nonregularity, but with an asymptotic variance that must be adjusted for the cross-fold correlation. Then, I propose a method for estimating this correlation and construct new confidence intervals that attain asymptotically nominal coverage. Finally, I show that the proposed confidence intervals attain approximately nominal coverage in a simulation study with random forests and neural networks.

A Residual Tree Gaussian Process Modeling Framework for High-Dimensional Data

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02893v1 Announce Type: cross Abstract: With the advance of measurement technologies and increasing computing power, large spatial data with heterogeneous structures are often collected over high-dimensional domains. Existing Gaussian process (GP) models and computational strategies are often inadequate for analyzing such datasets in multi-dimensional domains. To address these challenges, we develop a Bayesian residual tree GP methodology called ResTGP for large spatial data with potentially heterogeneous structures in multi-dimensional domains. The key idea is to decompose a Gaussian process at a cascade of resolutions along a dyadic tree through iteratively computing predictive and residual processes so that the residual process on each tree node, both interior and leaf, becomes sufficient for the finer-level dependency within that node. This allows characterization of the underlying covariance structure in a flexible, multi-scale manner while achieving divide-and-conquer on the data domain, which leads to computational efficiency. To allow efficient tree inference, we introduce a computational strategy for Bayesian inference based on recursive message passing, which scales linearly with the sample size given the tree. This paper also proves posterior consistency of the model for estimating continuous functions in a nonparametric regression framework. Extensive numerical examples and the storm surge application confirm the advantages of the proposed method.

Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped. Existing analyses often impose restrictive assumptions on the estimated velocity field and yield convergence rates that fail to reflect the intrinsic low-dimensional structure common in real data, such as natural images and molecular geometries. In this work, we study the statistical generalization of flow-matching models for learning an unknown distribution $P_{\mathrm{data}}$ from finitely many samples. We derive finite-sample error bounds on the learned generative distribution, measured in the Wasserstein-$p$ distance, for all $p\geq 1$. Specifically, given $n$ i.i.d. samples from $P_{\mathrm{data}}$, we show that, for every $d>d_p^\ast(P_{\mathrm{data}})$ and appropriately chosen network architectures and hyperparameters, the learned distribution $\widehat{P}^{\mathrm{FM}}$ satisfies $ \mathbb{W}_p(\widehat{P}^{\mathrm{FM}},P_{\mathrm{data}}) \lesssim n^{-1/d}+n^{-1/(2p)}\bigl(\log(1/\xi)\bigr)^{1/(2p)}$ with probability at least $1-\xi$, where $d_p^\ast(P_{\mathrm{data}})$ denotes the Wasserstein-$p$ dimension of the target measure. Our results demonstrate that flow matching naturally adapts to the intrinsic geometry of data and mitigates the curse of dimensionality, as the convergence exponent depends on the intrinsic rather than ambient dimension. These guarantees remain meaningful in high-dimensional regimes and provide a theoretical explanation for the empirical success of flow matching on structured data distributions under substantially more relaxed assumptions than those in existing analyses.

Unifying Privacy Accounting: Information Equivalence and Information Loss

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02414v1 Announce Type: cross Abstract: Differential privacy (DP) admits several notions, but the choice among them may affect both privacy analysis and utility. In this paper, we consider four mainstream curve-based privacy notions within a unified information-theoretic framework. For a fixed ordered pair of output distributions, we establish information equivalence among the two directional privacy profiles of $(\varepsilon,\delta)$-DP, the pair of hypothesis-testing trade-off functions, and the extended privacy-loss distribution. The exact R\'enyi differential privacy (RDP) curve joins this equivalence class whenever it is finite at some order greater than one. Under this mild condition, choosing among these notions changes only their semantic interpretation and computational requirements. In contrast, taking the maximum of the directional privacy profiles or compressing the RDP curve into a single zero-concentrated differential privacy (zCDP) parameter can lose information. We quantify the information loss between the exact RDP curve and its zCDP bound for standard noise mechanisms. This gap is zero for Gaussian noise but generally positive for Gaussian-mixture, Laplace, discrete Gaussian, and Poisson-subsampled Gaussian mechanisms. Moreover, this gap grows linearly with the number of independently composed mechanisms. Our information-theoretic perspective has practical consequences. At the same certified privacy level, retaining the full RDP curve rather than using zCDP reduces the required noise variance by up to $45\%$ for Gaussian-mixture noise in workloads comparable in size to the American Community Survey. For DP-SGD on Fashion-MNIST under Poisson subsampling, an RDP-based privacy accountant improves test accuracy by up to $8.73$ percentage points compared to a zCDP-based accountant when both are calibrated to the same $(\varepsilon,\delta)$ guarantee.

Expected Utility Regret Rule: Minimax and Bayes Optimal Portfolio Choice

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02290v1 Announce Type: cross Abstract: This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.

Bayesian Operator Learning: Posterior Existence and Convergence of Point Estimates for Gaussian Priors

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03666v1 Announce Type: new Abstract: We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map $g_0:\mathcal{X}\to\mathcal{Y}$ between separable Hilbert spaces, we study the recovery of $g_0$ from $n\in\mathbb{N}$ noisy input-output pairs $(\boldsymbol{X},\boldsymbol{Z})=(X_i,Z_i)_{i=1}^n$ with $Z_i= g_0 (X_i ) + E_i$. Here the $X_i\in\mathcal{X}$ are randomly drawn 'design' points in a compact subset of $\mathcal X$, and the $E_i$ are assumed to be i.i.d. draws from a Gaussian white noise process indexed by $\mathcal{Y}$. For any 'operator-valued' prior $\mathbb{P}_G$ supported on the space of continuous operators, we show existence of the posterior $\mathbb P_{G|(\boldsymbol{X},\boldsymbol{Z})}$ as a regular conditional distribution, and provide a characterization of its Radon-Nikodym derivative. For Gaussian priors, we establish algebraic (in the sample size $n$) convergence rates for the posterior mean towards the ground truth; this corresponds to a ridge regularized kernel estimator. Moreover, we show that the posterior mean is minimax optimal (up to logarithmic factors) over hyperrectangles when the smoothness of the prior matches that of the ground truth. To illustrate the applicability of our analysis, we derive explicit learning rates for the Darcy flow solution operator.

Spatial Functional $k$-Nearest-Neighbour Regression under Polynomial Dependence

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02921v1 Announce Type: new Abstract: This paper investigates non-parametric regression estimation when the explanatory variable takes values in a separable Hilbert space and observations are sampled over an increasing regular spatial lattice. Under a rigorous field-to-field independence setup between covariates and errors, we explore the structural and asymptotic concentration properties of the functional $k$-nearest-neighbour ($k$-NN) estimator. By establishing a sharp pathwise deterministic sandwiching framework for the data-driven random bandwidth, we successfully decouple the local infinite-dimensional small-ball profile from the polynomial covariance decay of the neighborhood indicators. Pointwise convergence rates are derived across short-range, critical, and long-range spatial regimes, revealing a combined penalty term that reflects both covariate spatial interaction and response error memory. Furthermore, uniform consistency over compact subsets is established for unbounded sub-Gaussian error processes through metric entropy and indicator boundary shell chaining. Structured polynomial simulations confirm our theoretical rates and exemplify the precise mechanics of the spatial long-range bottleneck.

Characterizing Identifiability in Boolean Factor Models

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02682v1 Announce Type: new Abstract: Boolean factor models, including prominent subfamilies such as Boolean matrix decompositions and cognitive diagnosis models, find broad applications ranging from social sciences to engineering. Despite their flexibility, a key challenge lies in establishing the identifiability of their graphical structures, which specify how latent variables influence observed variables. Existing identifiability conditions typically rely on the strong assumption of pure nodes, which may be unrealistic in many applications. We develop a novel approach leveraging the Hasse diagram to represent the distribution of observed variables and transform identifiability into a graph isomorphism challenge. Based on this, we establish {\it sufficient and necessary} graphical identifiability conditions that do not require pure nodes. We further derive equivalent algebraic conditions and develop an efficient Boolean satisfiability (SAT)-based verification algorithm. We extend the analysis to probabilistic Boolean factor models, establishing conditions for jointly identifying the graphical structure and additional model parameters without requiring pure nodes. Our results substantially broaden the class of identifiable and interpretable Boolean factor models by removing the pure-node requirement, yielding new theoretical insights, while also providing practitioners with a concrete and easily implementable tool to assess model identifiability.

High-Dimensional Regularization of the Spatial Sign Covariance Matrix for Robust Shape Estimation

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.02633v1 Announce Type: new Abstract: Covariance estimation is a key component of many applications in system identification and data-driven control. Although heavy-tailed distributions may lack a covariance matrix to estimate, the shape matrix provides a well-defined, scale-free generalization for the broad family of elliptical distributions. In this setting, practitioners often employ Tyler's M-estimator (TME), which is defined implicitly and is computed using a fixed-point iteration. The spatial sign covariance matrix estimator (SSCM) offers a much simpler alternative: it corresponds to one iteration of TME. Yet, the SSCM has been largely regarded as an inferior estimator due to its statistical inconsistency under fixed-dimensional asymptotics. By contrast, using second-order tools from random matrix theory, we establish that, under standard assumptions, SSCM asymptotically dominates TME in Frobenius risk when dimension and sample size grow proportionally. This advantage arises from implicit regularization, which reduces variance at the cost of a bias that vanishes as the dimension grows. Numerical experiments support the theoretical predictions even at moderate dimensions.

Goodness-of-Fit Testing for Groupwise Spherical Error Structures

Mon, 05 Oct 2026 00:00:00 -0400

arXiv:2610.03469v1 Announce Type: new Abstract: The analysis of large data panels is important in econometrics and beyond. Prediction and inference methods for such data typically rely on simplifying model assumptions for the covariance structure of errors. One convenient assumption is what we call groupwise sphericity: that errors are uncorrelated across individuals and have constant variance within certain groups. While theoretically useful, in large panels groupwise sphericity is often too restrictive to apply in practice. We therefore develop new quantitative inference tools to test whether deviations from this model assumption are practically relevant. Our approach covers both large-dimensional data matrices and regression panels, in a regime where the cross-sectional dimension is proportional to the sample size. The theory is based on the analysis of extreme eigenvalues of the empirical covariance matrix and uses recent advances in random matrix theory. Numerical experiments demonstrate accurate size control and good power in finite samples.

Randomized Spectral Inference for Hyperuniformity

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2609.27961v2 Announce Type: replace Abstract: We test hyperuniformity from one large realization of a stationary point process. Hyperuniformity is equivalent to the average $A_r$ of the structure factor over $B_r$ vanishing as $r\downarrow0$, so the target is a low-frequency average rather than the value of the structure factor at the origin, which need not exist. We estimate $A_r$ from squared Fourier coefficients at frequencies drawn uniformly from $B_r$; if these coefficients are asymptotically Gaussian at almost every fixed frequency, the squared coefficients converge to independent variables with mean $A_r$. Assuming $A_r=s+c r^\alpha+\varepsilon_r$ with $|\varepsilon_r|\leq Lr^\beta$ and given exponents $0 0$ as $R\to\infty$, then the number of sampled frequencies tends to infinity, and then $r\downarrow0$. Essentially free translation actions with completely positive entropy satisfy the Fourier assumption.

Notes on Forr\'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2603.24333v2 Announce Type: replace Abstract: Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes a strong global Markov property connecting transitional conditional independencies with suitable graphical separation criteria for directed mixed graphs with input nodes (iDMGs), together with a version of causal calculus for iDMGs in a general measure-theoretic setting. These notes aim to further illustrate the motivations behind this framework and its connections to the literature, highlight certain subtlies in the general measure-theoretic causal calculus, and extend the "one-line" formulation of the ID algorithm of Richardson et al. (Ann. Statist. 51(1):334--361, 2023) to the general measure-theoretic setting.

A new class of colored Gaussian graphical models with explicit normalizing constants

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2601.16945v2 Announce Type: replace Abstract: We study Bayesian model selection in colored Gaussian graphical models (CGGMs), which combine sparsity of conditional independencies with symmetry constraints encoded by vertex- and edge-colored graphs. A key computational bottleneck in Bayesian inference for CGGMs is the evaluation of the Diaconis-Ylvisaker normalizing constants, given by gamma-type integrals over cones of precision matrices with prescribed zeros and equality constraints. We introduce a new subclass of RCON models for which these normalizing constants admit closed-form expressions. On the algebraic side, we identify conditions on the space of colored precision matrices that guarantee tractability of the associated integrals, leading to the notions of Block-Cholesky spaces (BC-spaces) and Diagonally Commutative Block-Cholesky spaces (DCBC-spaces). On the combinatorial side, we characterize the colored graphs inducing such spaces via a color perfect elimination ordering and a 2-path regularity condition, and define the resulting Color Elimination-Regular (CER) graphs and their symmetric variants. Our framework extends the theory of uncolored decomposable graphs to the colored setting, and the CER class contains all RCOP models associated with decomposable graphs. For models with a single vertex color, our framework reveals a close connection between DCBC-spaces and Bose-Mesner algebras. For models defined on BC-spaces, we derive finite product formulas for the normalizing constants in terms of gamma functions, matrix determinants, and model-specific structure constants. For RCON models whose matrix spaces are DCBC-spaces, we provide efficient methods for computing all structure constants and determinant factors required to evaluate these formulas. Our results substantially broaden the range of CGGMs amenable to Bayesian structure learning in high-dimensional applications.

How many labelers do you have? A closer look at gold-standard labels

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2206.12041v3 Announce Type: replace Abstract: The construction of most supervised learning datasets revolves around collecting multiple labels for each instance, then aggregating the labels to form a type of "true" label. We question the wisdom of this pipeline by developing a (stylized) theoretical model of this process and analyzing its statistical consequences, showing how access to non-aggregated label information can make training well-calibrated models more feasible than it is with cleaned labels. The entire story, however, is subtle, and the contrasts between aggregated and fuller label information depend on the particulars of the problem, where estimators that use aggregated information exhibit robust but slower rates of convergence, while estimators that can effectively leverage all labels converge more quickly if they have fidelity to (or can learn) the true labeling process. The theory makes several predictions for real-world datasets, including when non-aggregate labels should improve learning performance, which we test to corroborate the validity of our predictions.

Markov chain Monte Carlo for predictively oriented posteriors

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01818v1 Announce Type: cross Abstract: The predictively oriented posterior offers principled uncertainty quantification, even under model misspecification. However, it does not admit an explicit density and therefore cannot be computed using classical Monte Carlo sampling algorithms. We remedy this by deriving an approximation to the predictively oriented posterior whose density can be evaluated point-wise, and whose approximation error decays rapidly. These results are illustrated on case studies from epidemiology, spatial statistics, and low-energy nuclear physics.

Feature Selective Model Collapse in Diffusion Models: Total Replacement versus Fixed-Budget Training

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01318v1 Announce Type: cross Abstract: Model collapse arises when generative models are trained on synthetic data produced by earlier models. The phenomenon has attracted considerable attention because of its societal and technical implications. However, previous studies have reached seemingly contradictory conclusions: replacing real data with synthetic data causes collapse (Shumailov et al.), yet accumulating real data alongside synthetic data can prevent it. For diffusion models, we study an intermediate regime typical of finite-budget pipelines: all past datasets and the real data are kept, but each new model is trained on a fixed-size sample from this growing pool, so the real fraction vanishes without any data being removed. Experiments on a 2D spiral dataset as well as the image benchmarks (MNIST, Fashion-MNIST, and CIFAR-10) show that replacement protocol degrades dataset rapidly as in the literature, whereas the fixed budget degrades only partially, sparing some features. A linear-response model of the multi-generational parameter dynamics, analyzed by stochastic recursion, confirms that the two protocols differ: some features will be fragile and lost within a few generations for both protocols, while some will be robust and preserved over practically unbounded horizons under the fixed budget protocol.

Testing and segmentation of joint and individual components in integrative multi-source factor models

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01313v1 Announce Type: cross Abstract: Disentangling shared (joint) structures from source-specific (individual) variations is a fundamental task in multi-source data integration. Existing joint-individual models often rely on computationally intensive optimization or loose spectral bounds, leading to suboptimal separation accuracy and poor scalability. In this paper, we propose the Multi-Source Sequential Alignment Test (MSSAT). MSSAT leverages the geometric observation that true joint components manifest as closely aligned score subspaces across different data sources. By deriving the asymptotic null distribution of our alignment statistic, we develop a rigorous, resampling-free sequential testing procedure to accurately estimate the joint rank. Extensive simulations and real data applications, including a TCGA multi-omics dataset, demonstrate that MSSAT achieves superior separation accuracy and substantially faster computation compared to competing methods.

Counterfactual Generation via Flow Matching: Coupling-Sensitive End-to-End Rates

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01193v1 Announce Type: cross Abstract: Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual assignment mechanism. We develop a flow-matching approach that combines a sample-split, doubly robust training objective with a learned coupling between observed source outcomes and target outcomes drawn from a fitted conditional outcome model. To enable finite-step generation, we leverage a score-corrected stochastic sampler based on a Gaussian-smoothed interpolation. Our main theoretical contribution is a coupling-sensitive KL bound for constant-step Euler discretization: the error is controlled by moments of the source--target displacement under the chosen coupling, rather than by global uniform regularity of the velocity field, and has near-linear dependence on the ambient dimension. We also establish finite-sample non-parametric guarantees for the learned velocity and score fields when both the conditional outcome model and the source-target coupling are estimated from data. These bounds separate approximation, coupling-replacement, nuisance-estimation, generalization, and Monte Carlo errors and, combined with the sampler analysis, yield an end-to-end guarantee for counterfactual generation. Experiments on synthetic and semi-synthetic image benchmarks support the coupling-dependent theory and show that, at finite discretization budgets, the stochastic sampler can outperform the corresponding deterministic ODE sampler.

Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01088v1 Announce Type: cross Abstract: The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions. The maximizing mixing distribution can be nonunique, and the classical bound on its number of atoms grows linearly with the sample size $n$. We show that a vanishingly small random perturbation of the likelihood yields exact polylogarithmic sparsity. The resulting randomly reweighted NPMLE maximizes a weighted likelihood whose independent weights, taken to be Gamma in our analysis, concentrate around one as $n$ grows. With high probability, it is unique, has $O\{(\log n/\log\log n)^d+\log n\}$ atoms in dimension $d$, nearly maximizes the ordinary likelihood, and estimates the mixture density at a Hellinger rate that is parametric up to logarithmic factors. This sparsity holds for the estimator itself, not for an approximation of it, and requires no support penalty. The proof rests on an effective-dimension principle for positive kernel mixtures: low-dimensional variation of the fitted values controls the support of every extreme point of the set of maximizers. Numerical illustrations verify that the reweighted NPMLE has Hellinger risk and support size comparable to those of the ordinary NPMLE.

Uncertainty Quantification for Landweber Iteration with Randomized Normal-Operator Approximation

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00882v1 Announce Type: cross Abstract: Iterative methods are extremely popular for solving linear ill-posed inverse problems. While deterministic convergence, or more precisely, semi-convergence of such methods is widely studied, the problem of quantifying uncertainty in the resulting reconstructions due to random noise in the observed data has received far less attention. In this work, we study uncertainty quantification for the Landweber iteration in linear inverse problems using the Radon transform as a motivating example. We interpret the Landweber reconstruction statistically by analyzing how uncertainty in the measured data is propagated through the reconstruction map. This perspective is closely related to generalized fiducial inference, where uncertainty about the parameter is induced by inverting the relation between the observed data and the unknown (fixed) quantity. We combine the resulting stochastic uncertainty with a theoretical bound on the regularization bias to construct confidence intervals for the reconstructed solution. The evaluation of the resulting uncertainty estimates require repeated operations with the forward operator that can become expensive in large-scale problems. To reduce this cost, we use randomized singular value decomposition to obtain a low-rank approximation of the normal operator associated with the Radon transform and incorporate this approximation in quantifying uncertainty. {{In particular, this requires that the additional randomization error introduced due to the use of such randomized techniques be included in our approach for uncertainty quantification.}} Numerical results show that the proposed method provides accurate reconstructions and reliable uncertainty estimates at substantially reduced computational cost.

Discussion on "Principled type I error rate inflation in two-arm clinical trial designs with external control information borrowing" by Silvia Calderazzo, Manuel Wiesenfarth, Vivienn Weru, and Annette Kopp-Schneider

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00711v1 Announce Type: cross Abstract: Consideration of frequentist type-I error or power based on certain fixed conditions may not fully embrace the aims of a Bayesian analysis; this is particularly true in settings where informative priors are involved. Calderazzo et al. consider adaptations of a testing procedure involving Bayesian borrowing from external control data. Particular caution may be necessary here in order not to condition on parameters and data simultaneously. We consider their example case and argue that (a) the conditioning scheme may have limited practical implications, and (b) if the main concern are assumption violations, these might be better addressed by adapting the likelihood function.

Learning Local Fermionic Lindbladians under Parity Superselection

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00448v1 Announce Type: cross Abstract: Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\bar\alpha$, entrywise error $\varepsilon$ is achieved using $\widetilde{\mathcal{O}}(\bar\alpha^2\varepsilon^{-2}\log(m/\delta))$ samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error $\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\varepsilon$ per mode using $\widetilde{\mathcal{O}}_k(\bar\alpha^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/\delta))$ samples, under a supplied approximate coefficient-degree bound $\mathsf d$ and controlled weak-coefficient tails. All guarantees hold with probability at least $1-\delta$. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.

A Frame-Spread Lower Bound for Quantum Entropy Estimation under Fixed Rank-One Measurements

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00270v1 Announce Type: cross Abstract: We study estimation of the von Neumann entropy of a $d$-dimensional quantum state from independent outcomes of a fixed rank-one measurement. Let $\kappa_\nu\in[1,d+1]$ denote the normalized trace-zero frame spread; $\kappa_\nu=1$ for exact complex projective $2$-designs. For any fixed rank-one measurement and $n\le c_2d^2/\kappa_\nu$, the minimax mean-squared error is at least $c_1\log^2\{d^2/(\kappa_\nu n)\}$. For bounded frame spread and every fixed $0

Minimax Quantum State Tomography with Periodic Clifford Measurements

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00210v1 Announce Type: cross Abstract: Quantum state tomography provides a foundation for characterizing state preparation and predicting measurement outcomes. We characterize the minimax expected trace norm risk of quantum state tomography over classes with polynomial spectral decay under randomized nonadaptive single copy measurements. Under an explicit sufficient block size condition for the two layer periodic Clifford ensemble, we establish statewise expected trace norm oracle inequalities for operator norm minimum distance and measurement weighted projected least squares, with bounds that depend on each state's actual spectral tail, while the estimators require no prior knowledge of the state's structural characteristics, including its rank, eigenbasis, or spectral structure. Over these polynomial spectral decay classes, both estimators attain the minimax expected trace norm rates up to constants. As a direct consequence, the same estimators attain the minimax rate over every fixed rank constrained class, while remaining adaptive to the unknown structural characteristics of the state. For admissible logarithmic block sizes, the periodic Clifford measurements attain these guarantees with logarithmic elementary gate depth. The main technical ingredient is a uniform bound on the fourth moment of projectors for the periodic Clifford ensemble. The bound is sharp in dimension and holds for arbitrary test states, including those entangled across blocks. Covariance concentration and positivity yield adaptive oracle bounds, while a shared rotation information argument on spectral tail packings establishes matching lower bounds. We also provide polynomial time reconstruction algorithms, numerical comparisons, and Lean formalizations of all labeled theoretical results.

Sample complexity bounds for categorical Markov random fields via Discrete Diffusions

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.02128v1 Announce Type: new Abstract: Many applications in statistics, economics, and physics require sampling from high-dimensional categorical distributions with local dependence structures. Examples include finite memory language models, Ising and Potts systems in statistical physics and protein folding, etc. In modern machine learning, discrete diffusions have emerged as a flexible approach for sampling such data, with strong empirical performance. Motivated by this, we develop learning methods with end-to-end sample complexity bounds for discrete diffusion with uniform noising under local dependence, which we model through low order Markov random fields (MRFs). Our main technical insight is a new \emph{pinning decomposition} of the discrete score. It shows that unlike in continuous diffusions, the score decomposes into components where the dependence on time separates multiplicatively from the dependence on the target. Building on this decomposition, we propose a \emph{weight-sharing neural score learner} and combine it with $\tau$-leaping to obtain an end-to-end sampling procedure. Rather than treating score-learning error as a black-box input, as is common in existing sampling analyses, we study the score learning error from finite data and derive optimal sampling guarantees with explicit dependence on the vocabulary size, the interaction order of the MRF, and the sample size. Moreover, our strategy trains a single score network across uniform noise levels while leaving the sampling discretization to be chosen at inference-time. This allows the same trained model to trade accuracy for computational cost as inference-time budgets vary. Numerical experiments on Potts, Ising, and tree-structured models show that weight-sharing score networks outperform fully connected ones for sampling long sequences.

User-friendly approximation theory for statistical regression

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01342v1 Announce Type: new Abstract: The error of regression using noisy function values naturally decomposes into an approximation error from the choice of model space and stochastic error from the noise on the observations. Statistical theory is mostly concerned with the stochastic error while approximation theory focuses on the approximation error, often subject to the assumption of noiseless observations. We combine the tools from approximation theory and statistics into a framework for bounding both errors in generalized least squares regression. The results cover weighted sup-norms and $L^2(\mu)$-norms, real- and complex-valued functions, and correlated noise under a range of tail and moment assumptions. Weighted Lebesgue functions and constants control the amplification of the best approximation error, while concentration inequalities provide bounds on the stochastic error. We organize these results into reusable bounds with explicit constants and establish sharpness where possible. For the common strategy of randomized regression we prove concentration of the Lebesgue function and constant around those of the corresponding $L^2(\mu)$-projection. For Fourier and Chebyshev regression on standard sampling grids, we obtain explicit, asymptotically tight $\mathcal O(\log m)$ bounds on the Lebesgue constants where $m$ is the model dimension. This improves upon the previous $\mathcal O(\sqrt{m})$ bound obtained for the regression setting and matches the bounds known for interpolation. A catalogue of approximation bounds and worked examples illustrates how to turn these results into explicit regression guarantees.

Cost Comparisons for Random and Deterministic Scans in Component-Wise Markov Chains

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01121v1 Announce Type: new Abstract: Gibbs samplers, and more generally component-wise Markov chain Monte Carlo algorithms such as Metropolis-within-Gibbs, can be implemented using either random-scan or deterministic-scan updates. How much convergence can depend on this choice of scanning rule has been a longstanding question. We study this problem through $L^2$ spectral gaps, measuring computational cost in units of component updates. For a $d$-block Gibbs sampler, the cost of random scan is at most twice that of any fixed deterministic scan, while the reverse cost ratio is at most of order $d^2$. We extend these comparisons to general reversible component-wise updates under the global block-wise contraction condition. If $K_j$ denotes the update of block $j$ and $P_j$ its Gibbs counterpart, and $\|K_j-P_j\|\leq \lambda_0<1$ for $j=1,\ldots,d$, then the cost of random scan is at most $2/(1-\lambda_0)$ times that of deterministic scan, while the reverse cost ratio is of order at most $d^2/(1-\lambda_0)$. Examples show that the cost bounds for random scan relative to deterministic scan are asymptotically sharp and that the joint dependence on $d$ and $(1-\lambda_0)^{-1}$ in the reverse comparison cannot be improved uniformly. This work was assisted by generative AI, including for formal verification of mathematical results in Lean. The human author reviewed and verified the mathematical content and takes full responsibility for the results.

Gradient-Guided Density Peak Clustering

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01050v1 Announce Type: new Abstract: Density peak clustering (DPC) connects each observation to its nearest neighbor of higher density and identifies cluster centers as high-density observations with unusually large nearest neighbor uphill shifts. The resulting uphill paths from observations to cluster centers, however, can be irregular and unstable in low-density regions, making the clustering assignments sensitive to local perturbations and obscuring the population geometry of the DPC graph. In this paper, we introduce \emph{gradient-guided density peak clustering} (GGDPC), which performs a gradient ascent step before each nearest neighbor uphill search. We develop a stability theory that relates the GGDPC graph to the gradient ascent flow of the population density. In particular, we establish consistency of GGDPC under five complementary criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. Together, these results provide new statistical, geometric, and topological interpretations of DPC-type clustering algorithms.

Integration of external predictions for efficient estimation of the risk ratio

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00769v1 Announce Type: new Abstract: We consider the augmentation of randomized experiments or trials with data from observational studies for the purpose of improving statistical precision. In particular, we focus on the Hybrid Augmented Inverse Probability Weighting estimator, designed to integrate predictions from several foundation models while preserving valid statistical inference. In this article, we extend the Augmented Inverse Probability Weighting framework to the estimation of the risk ratio, the quotient of the absolute risk of an exposed to an unexposed group. Our approach allows one to use information from black-box foundation models trained on external and possibly unstructured data, yielding an estimator of the risk ratio whose asymptotic variance is never larger than the one of the default estimator based on experimental data alone.

Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2604.11300v2 Announce Type: replace Abstract: We study the problem of modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model while permitting the presence of multiple structural change points. Such data call for a method that (i) handles high dimensionality and complex dependence while achieving consistency in multiple change points and further, (ii) addresses a unique challenge posed by the multi-dimensional array setting, of identifying the modes associated with each change while the shifts in different modes interact with one another. To this end, we propose a change point detection procedure utilizing the low-rank structure of the data for statistical and computational efficiency. In addition, we formalize the $\textit{mode-identifiability}$ of each change and propose an algorithm for detecting the modes at which the data undergo a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. We also analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods.

Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00515v1 Announce Type: new Abstract: Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fractional Laplace neural operator (fLNO) that embeds this structure in the learned map. For commuting excitation--Laplacian pairs, one block graph-spectral layer represents the full linear Volterra solution operator exactly. We establish an expressivity frontier for finite rational realizations: they approximate fractional memory geometrically on compact frequency windows, but cannot reproduce the non-integer critical asymptotics generated by a branch point, and on the half-line the best rational rate is root-exponential. The same theory yields trainable parametrizations that enforce a prescribed stability margin by construction, and a graphon-transfer theorem separates genuine operator consistency from parameter sharing. In a common-data benchmark, positive rational operators can match or exceed fLNO accuracy on finite horizons, whereas in controlled near-critical experiments fLNO recovers the branching coordinate more faithfully with far fewer parameters; unconstrained rational fits can cross the stability boundary, while certified parametrizations cannot. A four-parameter spectral law transfers without retraining from graphs of size 48 to 192 with 0.51--0.62% relative error. Applications to Chilean aftershock sequences and to renewal models for Chile and 21 Italian regions illustrate structured inference with explicit uncertainty. The contribution is an operator-learning architecture in which exact memory structure, physical coordinates and stability guarantees coexist with competitive accuracy.

Adaptive Conformal Prediction for Image Regression Models with Application to an Inertial Confinement Fusion Emulator

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00535v1 Announce Type: new Abstract: Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes settings. In many such applications, model outputs inform costly decisions, yet most methods provide only point estimates without quantifying predictive uncertainty. This challenge is compounded by the limited accessibility and interpretability of model internals, making it difficult to assess reliability across different regions of the input space. As a result, there is a growing need for methods that can provide input-dependent uncertainty estimates to guide both model development and downstream experimentation. To address this need, we propose Adaptive Conformal Prediction using Nearest Neighbors (ACPNN), an input-adaptive conformal framework for image regression. ACPNN leverages information from neighboring samples to produce locally adaptive uncertainty estimates while maintaining low computational cost. The neighborhood structure is defined using a scaled distance metric learned via a Gaussian Process with an automatic relevance determination (ARD) kernel. We demonstrate the effectiveness of ACPNN on a diffusion model for emulating inertial confinement fusion (ICF) simulations, showing that it achieves reliable and adaptive uncertainty quantification.

Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00793v1 Announce Type: new Abstract: We consider the estimation of drift, diffusion, and noise covariance from discrete observations of stochastic differential equations driven by Gaussian processes. For a fixed observation horizon $T>0$ and a known initial state $x_0\in\mathbb R$, we study \begin{equation*} dX_t=a(X_t)\,dt+\sigma(X_t)\,dZ_t^{\beta,f}, \qquad X_0=x_0,\quad 0\leq t\leq T. \end{equation*} \smallskip\noindent Here $a:\mathbb R\to\mathbb R$ is the drift coefficient, $\sigma:\mathbb R\to(0,\infty)$ is the diffusion coefficient, and $Z^{\beta,f}$ is a centered Gaussian process from the weighted sub-fractional Brownian family, with covariance \begin{equation*} \operatorname{Cov}(Z_s^{\beta,f},Z_t^{\beta,f}) =\int_0^{s\wedge t} f(r)q_\beta(s-r,t-r)\,dr, \qquad 0\leq s,t\leq T. \end{equation*} \smallskip\noindent Here $s\wedge t=\min\{s,t\}$. The temporal weight $f:[0,T]\to[0,\infty)$ is measurable, bounded, and positive almost everywhere, and $\beta\in(0,2)$ is the covariance exponent. For $u,v\geq0$, the kernel is $q_\beta(u,v)=[u^\beta+v^\beta-(u+v)^\beta]/(1-\beta)$ when $\beta\ne1$. Its continuous extension at $\beta=1$ is $q_1(u,v)=(u+v)\log(u+v)-u\log u-v\log v$, with $0\log0=0$. Using the Euler approximation, we reconstruct the Gaussian driving increments from observed transitions and use their joint density to obtain a trajectory likelihood. Neural and radial-basis representations model the drift, diffusion, and normalized temporal weight, while a likelihood profile estimates the covariance exponent and diffusion scale. We compare the method with two neural alternatives on the same simulated trajectories in twenty coefficient settings.

Block Optimism for Nonstationary Bandits with Latent Linear Dynamics

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00911v1 Announce Type: new Abstract: We study an endogenous nonstationary stochastic bandit problem with latent linear dynamics, where actions affect both immediate rewards and the future evolution of an unobserved latent state. Rewards are bilinear in the current action and latent state, inducing history-dependent rewards and a nontrivial long-horizon planning problem. The existing explore-then-commit approach achieves $\tilde{O}(T^{2/3})$ regret by uniformly exploring to estimate the latent dynamics and then committing to an optimized open-loop action sequence. We show that this rate can be improved via adaptive block-level optimism. Our key step is a cyclic approximation: under stable dynamics, the infinite-memory reward process can be truncated, and the open-loop benchmark can be approximated by optimizing a finite-memory block-level proxy. Building on this reduction, we propose a UCB-based block algorithm that maintains confidence sets for the truncated dynamics parameters and selects blocks optimistically. We prove a regret bound of order $\tilde{O}(\sqrt T)$, significantly improving over the previous $\tilde{O}(T^{2/3})$ guarantee for the same model. To the best of our knowledge, this is the first $\tilde{O}(\sqrt T)$ regret guarantee for latent linear-dynamics bandits with bilinear reward observations and an open-loop action-sequence benchmark.

The Price of Correlated Tests: How Strict Should a Model Release Gate Be?

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00993v1 Announce Type: new Abstract: Before a machine learning model ships, it often has to pass a suite of automated tests. Requiring every test to pass looks safe, yet it can reject many models that would have served users well, and it does not say how trustworthy a passing model actually is. We treat the release gate as a design problem: choose how many tests a model must pass so that cleared models meet a stated reliability target, while keeping as many good models as possible. A two-class latent-factor model makes both costs explicit and reduces each calculation to a one-dimensional integral. We prove that when both classes share the same latent correlation, a stricter gate always raises reliability, so the gate that keeps the most good models is the most lenient one that still meets the target. Under pass-all gating, any reliability target short of perfection is attainable within the model, but the share of good models kept tends to zero as the suite grows. Correlation between tests sets the price. In one configuration, a 99 percent target needs 8 independent tests, but 74 tests at a latent correlation of 0.3 and 5,182 at 0.5, where the gate keeps fewer than one good model in ten. We also give a validation procedure, built on exact binomial bounds, that certifies a gate from labelled data even when the gate is chosen from a fixed shortlist.

Tolerance-Based Fairness Auditing: Violation Certification and Sensitivity Screening

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01005v1 Announce Type: new Abstract: As artificial intelligence is increasingly deployed, algorithmic unfairness has raised growing concerns and intensified demands for transparent fairness auditing. In practice, the tolerable degree of algorithmic unfairness depends on the specific legal, ethical, or application context. Given a prespecified tolerance threshold, an important statistical question is how to determine whether a group disparity exceeds the allowable tolerance across different auditing objectives. To address this problem, we develop a unified tolerance-based fairness auditing framework for two complementary auditing objectives: violation certification, which prioritizes control of false violation declarations, and sensitivity screening, which prioritizes reducing missed violations. For the first objective, we develop a constrained empirical likelihood test for formal settings that uses least-favorable-point calibration and can be combined with false flagging rate control for simultaneous subgroup auditing. For the second objective, we develop split empirical likelihood and adjusted split empirical likelihood tests using an adaptive boundary-proxy principle for early-warning settings. Numerical experiments show the distinct error-control--sensitivity trade-offs of these procedures. A COMPAS analysis illustrates the framework in predictive fairness auditing.

ChainLoRA: Geometry-Preserving Task Vector Merging for Continual Learning in LLMs

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00431v1 Announce Type: new Abstract: Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present \textbf{ChainLoRA}, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

Optimal Transport Meets Reinforcement Learning: A Survey

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01413v1 Announce Type: new Abstract: Reinforcement learning (RL) algorithms frequently compare probability distributions, such as state visitation distributions induced by policies and experts, action distributions from learned policies and offline datasets, or transition distributions from learned models and environments. However, commonly used divergences may become ineffective when these distributions overlap weakly, which is frequently encountered in imitation learning, offline RL, and deployment under distribution shift. Optimal transport (OT) offers an alternative by measuring the cost of \emph{moving} probability mass from one distribution to another under a ground cost that encodes task geometry. This survey covers how OT is used inside RL objectives and algorithms. For each method, we identify: the role OT plays, the distributions compared, the OT formulation used, and the treatment of temporal structure. Beyond categorising existing methods, we discuss the motivations behind different OT choices, practical considerations such as cost design and computational challenges, and highlight open problems including scalable trajectory-level transport, principled handling of mass mismatch, and theoretical analysis for OT-regularised RL.

Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01472v1 Announce Type: new Abstract: Comparing two high-dimensional discrete distributions has always been a challenging task due to the exponentially growing state space and complex changes in interactions. A recent work suggests comparing distributions through a vector field trained using flow matching between two continuous distributions. The resulting vector field at mid-point vanishes if and only if two distributions identical. However, such a flow-based criterion does not naturally apply to discrete distributions. We extend this principle to the discrete domain and introduce the \emph{Zero Flux} criterion, a discrepancy based on local probability fluxes. Under independent coupling, we show that all local probability fluxes vanish at the midpoint if and only if two distributions are the same. This discrepancy decomposes the joint distributional difference into smaller, local contributions and can be efficiently estimated from samples. We establish finite sample error bounds for our estimator. Experiments on synthetic and real categorical data demonstrate reliable recovery of sparse dependence signals and stable tracking of distribution shifts in high dimensions.

Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.01933v1 Announce Type: new Abstract: Inference-time scaling adapts pretrained diffusion models to new sampling tasks without additional training. Existing methods rely primarily on Monte Carlo sampling with more particles, yet are premised on the pretrained model being exact. In practice, data and training limitations make the model imperfect, and these methods inherit its error. More particles reduce Monte Carlo error but cannot remove the mismatch between the endpoint and the desired target or the error in tracking the prescribed probability path. We introduce the Energy-based Feynman-Kac Corrector (EBFKC), a framework for energy-based diffusion models that corrects these errors on the fly given a reference energy. We first derive Feynman-Kac dynamics that track a prescribed path exactly in the continuous-time population limit even when the model is imperfect, and approximate these dynamics using sequential Monte Carlo with variance-controlling guidance. To remove the endpoint mismatch, we use the pretrained energy as a surrogate along the diffusion path and progressively incorporate the discrepancy between the learned and target terminal energies. Experiments on Gaussian mixture models, particle systems, alanine dipeptide, and alanine tetrapeptide show that our method closely matches target distributions and molecular free-energy profiles under annealing and reward tilting, whereas standard inference-time scaling baselines retain substantial sampling errors.

Partial AUC Maximization from Positive-unlabeled Data

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00284v1 Announce Type: cross Abstract: The partial area under the receiver operating characteristic curve (pAUC) is an important performance metric for binary classification that summarizes true positive rates within a specific range of false positive rates (FPRs). Classifiers that achieve high pAUC need to be obtained in many real-world applications such as cybersecurity, medical care, and advertising. Although many methods for maximizing the pAUC have been proposed, they typically require both labeled positive and negative data for training. However, in practice, labeled negative data are often difficult to collect due to privacy concerns or the need for high expertise to annotate them. In this paper, we propose a method for maximizing the pAUC from positive and unlabeled (PU) data without negative data. Within an empirical risk minimization framework, we show that the pAUC, including its FPR-dependent thresholds, can be represented using only the positive and marginal densities, and derive an empirical estimator from PU data. A classifier is then trained by maximizing the derived smoothed empirical pAUC estimator. We experimentally demonstrate the effectiveness of the proposed method with ten real-world datasets.

M$^2$Weather: A Benchmark for Joint Multi-Station and Multi-Variable Weather Forecasting

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00370v1 Announce Type: cross Abstract: Station weather forecasting is fundamentally shaped by both complex spatial dependencies across stations and strong physical coupling among weather variables. However, existing studies often consider these relationships separately and use different datasets and experimental settings, hindering systematic assessment of their individual and joint contributions. In this paper, we introduce $M^2$Weather, a benchmark for joint multi-station and multi-variable weather forecasting. Through multi-criteria quality control and station stratification, we collect 2,809 high-quality stations with 5 physically coupled weather variables across three spatial scales: France, Europe, and Global. This multi-scale design lets us examine whether conclusions persist from national to global station networks. We also introduce unified training and evaluation protocols to enable fair comparison of different station-variable modeling paradigms. To further examine the benefits of modeling station-variable relationships, we design a lightweight, plug-and-play adapter. With a trained weather forecasting model, this adapter can introduce missing station or variable relationships without retraining the model. This enables fair and efficient investigation of station-variable relationships. Systematic evaluation of 16 representative models shows the benefits of jointly modeling station and variable relationships. Completing missing relationships further reduces MSE for all adapted models on all three datasets. Together, these results identify the complementary information across stations and variables as an important resource for improving station weather forecasting. Our code can be obtained at https://github.com/hnu-vis/M2-Weather.

STCFormer: Adaptive Spatio-Temporal Modeling with Dynamic Cluster Transformer for Station-based Weather Forecasting

Fri, 02 Oct 2026 00:00:00 -0400

arXiv:2610.00377v1 Announce Type: cross Abstract: Station-based weather forecasting supports daily life and economic activity, yet accurate forecasts require modeling complex spatial dependencies among stations. Recent clustering-based selective modeling offers a promising alternative to dense inter-station interactions. However, a grouping shared across an observation window may obscure local changes in station relationships, while intra-cluster interactions alone may miss important global context. The theoretical advantages of selective interactions over dense connectivity also remain insufficiently understood. We therefore propose STCFormer, an adaptive spatio-temporal Transformer that dynamically groups stations according to their local evolution within each temporal patch. Its Cluster-Guided Attention Block combines fine-grained local attention within clusters and global attention over regional state summaries, allowing each station to access information beyond its own cluster. We further show that a derived Lipschitz upper bound for cluster-conditioned local attention is no larger than its fully connected counterpart, explaining a potential robustness benefit and motivating the design of InfoLoss. Experiments on three real-world weather datasets spanning eight temperature and wind forecasting tasks show that STCFormer achieves the lowest 24-hour mean squared error on all eight tasks and ranks first or second in 47 of 48 comparisons across metrics and forecasting horizons. Ablations and case studies further confirm the benefits of locally adaptive grouping and complementary local-global interactions. Our code can be obtained at https://github.com/hnu-vis/STCFormer.