统计机器学习：2025–2026 年度综述

An annual survey of the stat.ML arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 132 papers and organised into 37 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• Statistical Learning Theory and Neural Estimation (76.0%) — Develops statistical foundations and estimation methods for neural networks and machine learning models, including drift estimation, uncertainty quantification, and distributional analysis.
• Optimization and Stochastic Approximation (7.3%) — Studies convergence and efficiency of stochastic gradient methods, kernel-based optimization, and adaptive algorithms for risk minimization in high-dimensional settings.
• Large Language Model Alignment and Reasoning (4.7%) — Focuses on aligning LLM outputs with human preferences, improving reasoning capabilities, and evaluating model behavior through reinforcement learning and bandit frameworks.
• Bayesian Inference and Probabilistic Computation (4.6%) — Develops efficient Bayesian inference algorithms, including MCMC and variational methods, for complex probabilistic models with graphical or hierarchical structure.
• Conformal Prediction and Uncertainty Quantification (3.5%) — Provides distribution-free predictive guarantees and calibrated uncertainty estimates for machine learning models under distribution shift and finite-sample settings.
• Time Series Forecasting and Temporal Dependence (1.2%) — Addresses challenges in multivariate time series prediction, anomaly detection, and conformal inference under temporal dependence and nonstationarity.
• Physics-Informed Learning and Operator Methods (1.2%) — Integrates differential equations and structural constraints into neural models for solving inverse problems and learning solution operators.
• Sample Complexity and Finite-Size Analysis (0.9%) — Analyzes finite-sample behavior, sample complexity bounds, and practical scaling properties of learning algorithms in small-data regimes.
• Interpretable Classification and Detection (0.4%) — Develops interpretable methods for classification, anomaly detection, and scientific discovery, including change-point detection and out-of-distribution identification.
• Kernel Methods and Hypothesis Testing (0.2%) — Investigates kernel-based statistical tests, calibration procedures, and theoretical properties of learned representations for assessing model performance.
• Bias and Behavior in Deployed Models (0.1%) — Examines real-world biases, behavioral properties, and fairness issues in popular machine learning models, with emphasis on Shapley explanations and popularity alignment.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.