Regularization, sparse recovery, and median-of-means tournaments
This addresses robust regression estimation for heavy-tailed data, which is a domain-specific problem with incremental improvements over existing methods.
The authors tackled regression function estimation under heavy-tailed predictor and response variables by introducing a regularized risk minimization procedure based on median-of-means tournaments, achieving near optimal accuracy and confidence while outperforming standard methods like lasso or slope in such problems.
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.