Regularization, sparse recovery, and median-of-means tournaments

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-taile...

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Detalles Bibliográficos
Autores: Lugosi, Gábor, Mendelson, Shahar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/72104
Acceso en línea:http://hdl.handle.net/10230/72104
http://dx.doi.org/10.3150/18-BEJ1046
Access Level:acceso abierto
Palabra clave:Lasso
Median-of-means tournament
Regularized risk minimization
Robust regression
Slope
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spelling Regularization, sparse recovery, and median-of-means tournamentsLugosi, GáborMendelson, ShaharLassoMedian-of-means tournamentRegularized risk minimizationRobust regressionSlopeWe 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.Bernoulli Society for Mathematical Statistics and Probability2025202520192025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/72104http://dx.doi.org/10.3150/18-BEJ1046http://hdl.handle.net/10230/72104reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésBernoulli: Official Publication of the Bernoulli Society for Mathematical Statistics and Probability. 2019;25(3):2075-2106info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P© 2019 Bernoulli Society for Mathematical Statistics and Probabilityinfo:eu-repo/semantics/openAccessoai:recercat.cat:10230/721042026-05-29T05:05:01Z
dc.title.none.fl_str_mv Regularization, sparse recovery, and median-of-means tournaments
title Regularization, sparse recovery, and median-of-means tournaments
spellingShingle Regularization, sparse recovery, and median-of-means tournaments
Lugosi, Gábor
Lasso
Median-of-means tournament
Regularized risk minimization
Robust regression
Slope
title_short Regularization, sparse recovery, and median-of-means tournaments
title_full Regularization, sparse recovery, and median-of-means tournaments
title_fullStr Regularization, sparse recovery, and median-of-means tournaments
title_full_unstemmed Regularization, sparse recovery, and median-of-means tournaments
title_sort Regularization, sparse recovery, and median-of-means tournaments
dc.creator.none.fl_str_mv Lugosi, Gábor
Mendelson, Shahar
author Lugosi, Gábor
author_facet Lugosi, Gábor
Mendelson, Shahar
author_role author
author2 Mendelson, Shahar
author2_role author
dc.subject.none.fl_str_mv Lasso
Median-of-means tournament
Regularized risk minimization
Robust regression
Slope
topic Lasso
Median-of-means tournament
Regularized risk minimization
Robust regression
Slope
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019
2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/72104
http://dx.doi.org/10.3150/18-BEJ1046
http://hdl.handle.net/10230/72104
url http://hdl.handle.net/10230/72104
http://dx.doi.org/10.3150/18-BEJ1046
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv 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
dc.rights.none.fl_str_mv © 2019 Bernoulli Society for Mathematical Statistics and Probability
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2019 Bernoulli Society for Mathematical Statistics and Probability
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Bernoulli Society for Mathematical Statistics and Probability
publisher.none.fl_str_mv Bernoulli Society for Mathematical Statistics and Probability
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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