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There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

Machine Learning · Statistics 2022-10-12 Lihu Xu , Fang Yao , Qiuran Yao , Huiming Zhang

In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and…

Statistics Theory · Mathematics 2023-08-29 Miriam Hägele , Jaakko Lehtomaa

We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the $\ell_0$-norm of the mean change vector, we separately consider dense and sparse…

Statistics Theory · Mathematics 2025-10-14 Mengchu Li , Yudong Chen , Tengyao Wang , Yi Yu

In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…

Methodology · Statistics 2026-05-29 Herman Tesso , Georges Nguefack-Tsague

Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized…

Machine Learning · Computer Science 2026-02-23 Junfei Sun , Dixi Yao , Xuchen Gong , Tahseen Rabbani , Manzil Zaheer , Tian Li

We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary…

Machine Learning · Computer Science 2021-05-26 Tommaso d'Orsi , Gleb Novikov , David Steurer

Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments,…

Machine Learning · Computer Science 2026-03-23 Siddharth Chandak , Anuj Yadav , Ayfer Ozgur , Nicholas Bambos

We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…

Statistics Theory · Mathematics 2016-12-20 Lihua Lei , Peter J. Bickel , Noureddine El Karoui

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…

Statistics Theory · Mathematics 2018-07-04 Nicolas Auguin , David Morales-Jimenez , Matthew R. McKay , Romain Couillet

Randomized controlled trials (RCTs) are widely regarded as the gold standard for causal inference in biomedical research. For instance, when estimating the average treatment effect on the treated (ATT), a doubly robust estimation procedure…

Methodology · Statistics 2025-09-26 Chi-Shian Dai , Chao Ying , Yang Ning , Jiwei Zhao

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…

Econometrics · Economics 2026-01-21 Yoichi Arai , Taisuke Otsu , Myung Hwan Seo

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

Optimization and Control · Mathematics 2025-05-15 Jun Hu , Chao Sun , Bo Chen , Jianzheng Wang , Zheming Wang

High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…

Methodology · Statistics 2026-04-16 Long Feng

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…

Methodology · Statistics 2024-01-25 Qiang Sun

Real-world datasets commonly exhibit noisy labels and class imbalance, such as long-tailed distributions. While previous research addresses this issue by differentiating noisy and clean samples, reliance on information from predictions…

Machine Learning · Computer Science 2024-03-06 Ying-Hsuan Wu , Jun-Wei Hsieh , Li Xin , Shin-You Teng , Yi-Kuan Hsieh , Ming-Ching Chang

We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized…

Methodology · Statistics 2026-04-07 Long Feng , Xiaoyi Wang , Le Zhou

Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in…

Methodology · Statistics 2024-10-07 Assma Alghamdi , Taposh Banerjee , Jayant Rajgopal

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…

Machine Learning · Computer Science 2022-02-09 Deebul S. Nair , Nico Hochgeschwender , Miguel A. Olivares-Mendez

Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope…

Methodology · Statistics 2020-11-03 Le Zhou , R. Dennis Cook , Hui Zou

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…

Methodology · Statistics 2016-10-06 Jana Janková , Sara van de Geer