Probability & Statistics · Mathematics & Statistics
Statistics Theory
The newest papers in Statistics Theory that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
321 papers, from 31 August 2026 to 4 November 2026: 287 arXiv preprints and 34 OpenAlex records.
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Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples.Self-normalized Bernstein Inequalities for Regenerative Processes and Applications to Learning Without Independence
We prove a self-normalized Bernstein inequality for bounded functions of a regenerative process with independent, identically distributed marked cycles of finite mean length.Differentially Private Synthetic Data via Generalized Moment Matching
We study $(\varepsilon,δ)$-differentially private synthetic data for arbitrary databases of $n$ records in $[-1,1]^d$ under a specified integral probability metric (IPM).On the Accuracy of Approximate Leave-One-Out with Blockwise Nonsmooth Regularization in High-dimensions
Approximate leave-one-out (ALO) refers to methods that provide computationally efficient and statistically accurate approximations to leave-one-out risk estimation.Anytime-Valid Runtime Monitoring of Learned Barrier Certificates
Learned barrier certificates provide a principled mechanism for establishing safety of stochastic systems, but their validity may deteriorate during deployment when the underlying dynamics differ…Optimal aggregation in multiclass classification
This paper studies the problem of aggregation in multiclass classification, generalizing existing results for binary classification.Confessions of a Masked MDP
In reinforcement learning, one presumes the action set to be known ahead of time, and, thus, one must know if any state-action pairs are not permissible ahead of computations.Birthday Estimators Are Uniformly Optimal for Renyi Entropy
Collisions are a basic probe of unknown distributions, used for testing and for counting substructures in graphs, and they underlie Rényi entropy, a fundamental measure of uncertainty with…Local data augmentation for imbalanced binary classification
Facing imbalanced binary classification, we aim at maximizing the recall while limiting the proportion of false detections in the minority class.Gaussian Approximation of Besov Functions for Logistic Classification on Manifolds
We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$ without boundary and of intrinsic dimension…A Short Note on Algorithms For The Noisy $k$-XOR Problem
This mostly expository note studies the sample-noise regimes in which the testing problem for noisy $k$-XOR in dimension $n$ can be efficiently solved.Solving the Ho--Nguyen Conjecture for Gaussian Mixtures: Applications to Mixtures of Experts
Over-fitted Gaussian mixtures can contain many parameter configurations with nearly the same density, making the order of density cancellation central to their parameter-learning rates.Dimension-free comparison inequalities between $f$-divergences for Gaussian location mixtures
We establish dimension-free comparison inequalities between the Kullback-Leibler (KL) and $χ^2$-divergences and the squared Hellinger distance for Gaussian location mixtures with compactly supported…Semi-supervised learning on singular data sets
We propose to model singular data clouds by subanalytic sets, and develop an approach to semi-supervised learning in this setting.Transformers as Adaptive Kernel Learners across Tasks for In-Context Learning
Transformers have emerged as a dominant architecture in modern machine learning, with in-context learning (ICL) enabling models to adapt to new tasks by conditioning on prompts, without any…A Label Noise Robust Algorithm for Graph Data using Neighborhood Label Distribution
Graph Convolutional Networks (GCNs) have demonstrated exceptional performance on graph-structured data.Information-Geometric Blind Spots of Conformal Test Martingales
Conformal test martingales (CTMs) are e-processes for sequentially testing exchangeability via p-values produced by a conformity function $A$.Exact Tail Laws for Nonlinear SGD with Infinite-Variance Gradients
With infinite-variance gradient noise, SGD can have infinite expected excess objective even when most iterates are close to the optimum.Margin Certificates for Voting Classifiers under Mixing Dependence
Margin bounds explain why weighted votes generalize after training error vanishes, but dependent observations require concentration arguments that keep the dependence model and failure budget…A One-Sided McDiarmid-Type Inequality for Heavy Tails via Reverse KL Tensorization
We revisit McDiarmid's inequality, a central tool in statistical learning theory and algorithm analysis.