Related papers: High-dimensional robust regression under heavy-tai…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…