Probability & Statistics · Mathematics & Statistics
Statistics Theory
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321 papers, from 31 August 2026 to 4 November 2026: 287 arXiv preprints and 34 OpenAlex records.
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Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift
We study high-dimensional nonparametric regression under multisource covariate shift, where $\mathrm J$ sources of training data share a common regression function but differ in their covariate…Comparing tail forecasts: the number of exceedances is the sample size
When two forecasts of a tail, such as prediction intervals at high coverage, extreme quantiles or expected shortfall (ES), are compared by a consistent score, the score difference is known in…Self-regularization and structural adaptation of NPMLE for Gaussian mixture models in all dimensions
We establish structural properties of the nonparametric maximum likelihood estimator (NPMLE) for $d$-dimensional Gaussian mixtures whose means lie in a hypercube.The Geometry of Multitask Learning: Sharp Rates for Shared Subspace Estimation
Learning a shared subspace in multitask learning is an important statistical problem, yet exact rates remain poorly understood in many of the formal settings considered in the literature.Computer-Assisted Results for \(n\)-Sided Non-Transitive Dice Taking Face Values in \([n]\)
We consider non-transitivity among dice with \(n\) sides restricted to taking face values in the set \(\{1,\ldots,n\}\).Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics
We consider the tensor principal components analysis (tensor PCA) problem on the sphere, in which we are asked to recover an unknown vector in $\mathcal{S}_N=\{x\in\mathbb{R}^N:\lVert x\rVert^2=N\}$…Scalable Bayesian Quadrature via Operator-Adapted Features
Kernel methods face two recurrent bottlenecks: the cubic cost of inverting an $n\times n$ kernel matrix, as in kernel ridge regression, and the evaluation of kernel integrals, as required in kernel…Memorization Capacity of Invariant Convolutional Neural Nets
Neural networks are powerful memorizers which are often able to interpolate their training data even when the labels have been randomized.Orthogonal Inference for Conditional Z-Estimation without Cross-Fitting: A Distributional Nearest-Neighbor Approach
Estimating conditional parameters, such as heterogeneous treatment effects, often requires rich covariate adjustment, even when the parameters are reported along only a few dimensions.A Spectral Boundary for Independence Learnability
Learning independence is fundamental to statistical inference and machine learning, yet learning independence between entire time series by a test remains challenging when only a single observation…A Simple Presentation of Robust Membership Inference Attacks
In a membership inference attack, an attacker is given the data of a particular individual, and tries to determine if that individual was included in a particular dataset, given some kind of…Second-order Sinkhorn Geometry and $\sqrt{n}$-Inference
The Sinkhorn divergence, a debiased form of entropic optimal transport, has been widely used in various scientific disciplines due to its computational and statistical tractability.Wasserstein approximation of measures via orthogonal frames: statistical and computational complexities
Dimension-reduction methods such as PCA identify a subspace capturing most of the variation in the data, but not a distinguished basis within it.Regression Functions as Fields on Covariate Space: Evolution Equations, the Hessian, and Identification
For each time $t$, the regression function $m_t(x)=E[Y_t\mid X_t=x]$ of an outcome on contemporaneous covariates can be regarded as a field on covariate space.Finite-Sample Optimal Conformal Prediction Sets under Covariate Shift
We study conformal prediction under covariate shift with a known covariate density ratio, seeking prediction sets with minimum expected length under the target distribution.Spectral delocalization and central limit theorems for Fourier functionals of stationary Gaussian fields
We characterize Gaussian fluctuations of Fourier-Hermite functionals of stationary Gaussian fields on locally compact Abelian groups via spectral delocalization: conditional on the total spectral…On the asymptotic behaviour of $α$-divergence generalized posteriors
We study the asymptotic behaviour of the solutions to the unconstrained generalized variational inference problem regularized by an $α$-divergence.Minimax Rates for Conditional Generative Learning under Wasserstein Loss
We study minimax rates for conditional generative learning under integrated Wasserstein loss, with Hölder continuous conditional laws and an unrestricted covariate distribution.Provably Efficient Q-learning for Robust Reinforcement Learning
Standard reinforcement learning (RL) algorithms based on Markov Decision Processes (MDPs) are vulnerable to sim-to-real gaps.Recertifying decisions via e-closure: uniform improvements of conformal risk control and randomized e-BH
Statistical procedures often control expected loss at a prescribed level while leaving part of their risk budget unused.