We introduce a regularized risk minimization procedure for regression function estimation. The procedure is based on median-of-means tournaments, introduced by the authors in Lugosi and Mendelson (2018) and achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. It outperforms standard regularized empirical risk minimization procedures such as LASSO or SLOPE in heavy-tailed problems.
"Regularization, sparse recovery, and median-of-means tournaments." Bernoulli 25 (3) 2075 - 2106, August 2019. https://doi.org/10.3150/18-BEJ1046