2026-04-14T07:20:52Zhttps://recercat.cat/oai/request

oai:recercat.cat:10230/721042025-12-06T17:21:49Zcom_2072_6col_2072_452952

Regularization, sparse recovery, and median-of-means tournaments Lugosi, Gábor Mendelson, Shahar Lasso Median-of-means tournament Regularized risk minimization Robust regression Slope 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. Gábor Lugosi was supported by the Spanish Ministry of Economy and Competitiveness, Grant MTM2015-67304-P and FEDER, EU; "High-dimensional problems in structured probabilistic models" -- Ayudas Fundacion BBVA a Equipos de Investigación Científica 2017; and Google Focused Award "Algorithms and Learning for AI". Shahar Mendelson was supported in part by the Israel Science Foundation. 2025-12-06T17:21:49Z 2025-12-06T17:21:49Z 2025-12-06T17:21:49Z 2025-12-02T14:22:31Z 2025-12-02T14:22:31Z 2019 2025-12-02T14:22:31Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://hdl.handle.net/10230/72104 Bernoulli: Official Publication of the Bernoulli Society for Mathematical Statistics and Probability. 2019;25(3):2075-2106 info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P © 2019 Bernoulli Society for Mathematical Statistics and Probability info:eu-repo/semantics/openAccess Bernoulli Society for Mathematical Statistics and Probability