# Regularization, sparse recovery, and median-of-means tournaments

## TL;DR

This paper introduces a regularized risk minimization method based on median-of-means tournaments that achieves near-optimal accuracy and confidence in regression, especially under heavy-tailed data distributions, outperforming standard methods.

## Contribution

The paper proposes a novel regularization technique using median-of-means tournaments that improves regression estimation under heavy-tailed conditions.

## Key findings

- Outperforms lasso and slope in heavy-tailed scenarios
- Achieves near-optimal accuracy and confidence
- Works under general conditions with heavy-tailed data

## Abstract

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.