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August 2019 Regularization, sparse recovery, and median-of-means tournaments
Gábor Lugosi, Shahar Mendelson
Bernoulli 25(3): 2075-2106 (August 2019). DOI: 10.3150/18-BEJ1046

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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Gábor Lugosi. Shahar Mendelson. "Regularization, sparse recovery, and median-of-means tournaments." Bernoulli 25 (3) 2075 - 2106, August 2019. https://doi.org/10.3150/18-BEJ1046

Information

Received: 1 November 2017; Revised: 1 April 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066250
MathSciNet: MR3961241
Digital Object Identifier: 10.3150/18-BEJ1046

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 3 • August 2019
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