Outlier Robust and Sparse Estimation of Linear Regression Coefficients

TL;DR

This paper introduces a new method for robustly estimating sparse linear regression coefficients that can handle adversarial outliers and heavy-tailed noise, providing sharper error bounds under weaker assumptions.

Contribution

It develops a novel estimation approach with improved theoretical guarantees for outlier-robust sparse linear regression under challenging data conditions.

Findings

Sharper error bounds achieved

Handles adversarial outliers effectively

Works under heavy-tailed noise distributions

Abstract

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.