English
Related papers

Related papers: Adaptive Huber Regression

200 papers

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

Statistics Theory · Mathematics 2017-05-15 Mogens Bladt , Leonardo Rojas-Nandayapa

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

We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…

Statistics Theory · Mathematics 2022-02-25 Jaouad Mourtada , Tomas Vaškevičius , Nikita Zhivotovskiy

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 propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…

Methodology · Statistics 2021-08-20 Y. Samuel Wang , Si Kai Lee , Panos Toulis , Mladen Kolar

A notoriously difficult challenge in extreme value theory is the choice of the number $k\ll n$, where $n$ is the total sample size, of extreme data points to consider for inference of tail quantities. Existing theoretical guarantees for…

Other Statistics · Statistics 2025-05-30 Johannes Lederer , Anne Sabourin , Mahsa Taheri

Real-world data is laden with outlying values. The challenge for machine learning is that the learner typically has no prior knowledge of whether the feedback it receives (losses, gradients, etc.) will be heavy-tailed or not. In this work,…

Machine Learning · Statistics 2020-12-16 Matthew J. Holland

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…

Statistics Theory · Mathematics 2018-11-07 Po-Ling Loh

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as…

Methodology · Statistics 2026-04-27 Dylan Dijk , Haeran Cho

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…

Methodology · Statistics 2020-12-10 Jaejoon Lee , Jaeyong Lee

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

Statistics Theory · Mathematics 2026-04-21 Alejandro Cholaquidis , Emilien Joly , Leonardo Moreno

Controlling the false discovery rate (FDR) is a critical challenge in large-scale data analysis, particularly in the presence of outliers. A common practice involves imposing a Student-$t$ distribution to eliminate the influence of…

Methodology · Statistics 2026-04-01 Yoshiko Hayashi

This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…

Econometrics · Economics 2024-08-08 Zhan Gao , Hyungsik Roger Moon

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient…

Data Structures and Algorithms · Computer Science 2021-01-20 Samuel B. Hopkins , Jerry Li , Fred Zhang

Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic…

Methodology · Statistics 2024-06-26 Xiaohui Yuan , Shujie Ren

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…

Methodology · Statistics 2020-09-21 Xi Chen , Weidong Liu , Xiaojun Mao , Zhuoyi Yang

Biclustering is widely used in different kinds of fields including gene information analysis, text mining, and recommendation system by effectively discovering the local correlation between samples and features. However, many biclustering…

Methodology · Statistics 2023-10-10 Yifan Chen , Chunyin Lei , Chuanquan Li , Haiqiang Ma , Ningyuan Hu

We study robust regression under a contamination model in which covariates are clean while the responses may be corrupted in an adaptive manner. Unlike the classical Huber's contamination model, where both covariates and responses may be…

Statistics Theory · Mathematics 2026-04-07 Ilias Diakonikolas , Chao Gao , Daniel M. Kane , Ankit Pensia , Dong Xie

This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function…

Statistics Theory · Mathematics 2021-05-26 Debarghya Mukherjee , Moulinath Banerjee , Ya'acov Ritov

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

Machine Learning · Computer Science 2018-10-26 Lijun Zhang , Zhi-Hua Zhou