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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
High-dimensional Gaussian and bootstrap approximations fo...
[Submitted on 11 Apr 2025 (v1), last revised 29 Jun 2026 (this v · 2025-04-11 · via stat updates on arXiv.org

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Abstract:Recent years have witnessed much progress on Gaussian and bootstrap approximations to the distribution of sums of independent random vectors with dimension $d$ large relative to the sample size $n$. However, for any number of moments $m>2$ that the summands may possess, there exist distributions such that these approximations break down if $d$ grows faster than the polynomial barrier $n^{\frac{m}{2}-1}$. In this paper, we establish Gaussian and bootstrap approximations to the distributions of winsorized and trimmed means that allow $d$ to grow at an exponential rate in $n$ as long as $m>2$ moments exist. The approximations remain valid under some amount of adversarial contamination. Our implementations of the winsorized and trimmed means do not require knowledge of $m$. As a consequence, the approximation guarantees ``adapt'' to $m$.

Submission history

From: David Preinerstorfer [view email]
[v1] Fri, 11 Apr 2025 10:51:00 UTC (28 KB)
[v2] Tue, 3 Jun 2025 14:11:44 UTC (29 KB)
[v3] Thu, 6 Nov 2025 10:46:29 UTC (30 KB)
[v4] Thu, 26 Mar 2026 15:00:53 UTC (554 KB)
[v5] Mon, 29 Jun 2026 14:40:14 UTC (556 KB)