Clay weekly context brief for the Statistics category (ISO week 2026-W29). Clay tracks publications from the Statistics feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed. Recent publications: 1. Accelerating Large Language Model Inference with Self-Supervised Early Exits Source: stat.ML (Machine Learning) Link: https://arxiv.org/abs/2407.21082 This paper presents a modular approach to accelerate inference in large language models (LLMs) by adding early exit heads at intermediate transformer layers. 2. A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives Source: stat.CO (Computation) Link: https://arxiv.org/abs/2509.10393 Several methods in statistics and machine learning target a probability distribution for which an entropy-regularised variational objective is minimised. 3. Exclusivity Classes and Partitions of Loss Functions Source: stat.TH (Statistics Theory) Link: https://arxiv.org/abs/2507.12447 Loss functions define estimator optimality, yet current decision-theoretic tools say little about when different losses demand incompatible optimal procedures. 4. Predicting fixed-sample test decisions enables anytime-valid inference Source: stat.ME (Methodology) Link: https://arxiv.org/abs/2602.13872 Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. 5. Accelerated Fully First-Order Methods for Bilevel and Minimax Optimization Source: stat.ML (Machine Learning) Link: https://arxiv.org/abs/2405.00914 We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO). 6. XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Source: stat.CO (Computation) Link: https://arxiv.org/abs/2605.13922 During thDuring the last few years, the term Mechanistic Interpretability, a specific area, under the umbrella of explainable artificial intelligence (XAI), has been introduced, to explain the decisions made by complex machine learning (ML) models in critical systems like UAV intrusion detection systems (UAVIDS). 7. Gaussian approximation for non-linearity parameter estimation in perturbed random fields on the sphere Source: stat.TH (Statistics Theory) Link: https://arxiv.org/abs/2507.05074 We develop a probabilistic framework for the asymptotic analysis of a bispectrum-based estimator of primordial non-Gaussianity for isotropic random fields on the sphere in the high-resolution regime. 8. Optimal Spatial Anomaly Detection Source: stat.ME (Methodology) Link: https://arxiv.org/abs/2510.22330 There has been a growing interest in anomaly detection problems recently, whilst their focuses are mostly on anomalies taking place on the time index. 9. Hierarchical Causal Models Source: stat.ML (Machine Learning) Link: https://arxiv.org/abs/2401.05330 Causal questions often arise in settings where data are hierarchical: subunits are nested within units. 10. Fast and accurate conditioning for large-scale Gaussian process prediction problems Source: stat.CO (Computation) Link: https://arxiv.org/abs/2605.02574 Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. 11. Confidence Intervals Using Turing's Estimator: Simulations and Applications Source: stat.TH (Statistics Theory) Link: https://arxiv.org/abs/2503.14313 Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. 12. Counting on count regression: a reexamination of routinely-cited Negative Binomial specifications Source: stat.ME (Methodology) Link: https://arxiv.org/abs/2407.05824 Negative Binomial regression is a staple in empirical management research, especially for the analysis of supply chain disruption risks. 13. Kernel of Partition Paths: A Unified Representation for Tree Ensembles Source: stat.ML (Machine Learning) Link: https://arxiv.org/abs/2606.18853 A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and feature-importance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. 14. Testing MCAR via covariances: Extending the U-statistic framework to partially observed variables Source: stat.TH (Statistics Theory) Link: https://arxiv.org/abs/2501.05596 This paper presents a generalized version of a U-statistics-based test for MCAR developed by Aleksi\'c (2024). 15. Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model Source: stat.ME (Methodology) Link: https://arxiv.org/abs/2403.05359 Using Non-negative Matrix Factorization (NMF), an observed matrix is approximated by a basis matrix times a coefficient matrix. 16. Tuning Derivatives for Causal Fairness in Machine Learning Source: stat.ML (Machine Learning) Link: https://arxiv.org/abs/2605.05882 Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. 17. Misspecification Analysis of High-Dimensional Random Effects Models for Estimation of Signal-to-Noise Ratios Source: stat.TH (Statistics Theory) Link: https://arxiv.org/abs/2202.06400 Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications, including heritability estimation in bioinformatics. 18. Optimal monotone conditional error functions Source: stat.ME (Methodology) Link: https://arxiv.org/abs/2402.00814 This paper presents a general method that provides optimal monotone conditional error functions for confirmatory adaptive two-stage designs with conditional power based sample size recalculations. Sources in this brief: stat.CO (Computation); stat.ME (Methodology); stat.ML (Machine Learning); stat.TH (Statistics Theory). Selected 18 of 59 available items for this weekly brief.