Title: Regularization, sparse recovery, and median-of-means tournaments,
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.