Outlier-robust Estimation of a Sparse Linear Model Using Invexity

TL;DR

This paper introduces a robust method for sparse linear model estimation that effectively handles outliers by identifying clean samples and employing an invex relaxation with theoretical guarantees.

Contribution

It proposes a novel combinatorial outlier-robust lasso approach with an invex relaxation, improving support recovery and outlier detection in sparse regression.

Findings

The method accurately identifies outliers and clean samples.

The approach outperforms standard lasso in robustness and support recovery.

Theoretical guarantees validate the proposed relaxation.

Abstract

In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of outlier-robust lasso which also identifies clean samples. Subsequently, we use these clean samples to make a good estimation. We also provide a novel invex relaxation for the combinatorial problem and provide provable theoretical guarantees for this relaxation. Finally, we conduct experiments to validate our theory and compare our results against standard lasso.