Lugosi, GáborMendelson, Shahar2025-12-022025-12-022019Lugosi G, Mendelson S. Regularization, sparse recovery, and median-of-means tournaments. Bernoulli (Andover). 2019;25(3):2075-106. DOI: 10.3150/18-BEJ10461350-7265http://hdl.handle.net/10230/72104We 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.application/pdfeng© 2019 Bernoulli Society for Mathematical Statistics and Probabilityinfo:eu-repo/semantics/article2025-12-02http://dx.doi.org/10.3150/18-BEJ1046LassoMedian-of-means tournamentRegularized risk minimizationRobust regressionSlopeinfo:eu-repo/semantics/openAccess