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

Gábor Lugosi; Shahar Mendelson

doi:10.3150/18-BEJ1046

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

Gábor Lugosi, Shahar Mendelson

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2075-2106
Number of pages	32
Journal	Bernoulli
Volume	25
Issue number	3
DOIs	https://doi.org/10.3150/18-BEJ1046
Publication status	Published - 2019

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abstract = "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.",

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AB - 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.

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KW - Regularized risk minimization

KW - Robust regression

KW - SLOPE

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DO - 10.3150/18-BEJ1046

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

Abstract

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