Open Access
December 2015 Empirical risk minimization for heavy-tailed losses
Christian Brownlees, Emilien Joly, Gábor Lugosi
Ann. Statist. 43(6): 2507-2536 (December 2015). DOI: 10.1214/15-AOS1350


The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess risk. However, some robust mean estimators proposed in the literature may be used to replace empirical means. In this paper, we investigate empirical risk minimization based on a robust estimate proposed by Catoni. We develop performance bounds based on chaining arguments tailored to Catoni’s mean estimator.


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Christian Brownlees. Emilien Joly. Gábor Lugosi. "Empirical risk minimization for heavy-tailed losses." Ann. Statist. 43 (6) 2507 - 2536, December 2015.


Received: 1 June 2014; Revised: 1 May 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1326.62066
MathSciNet: MR3405602
Digital Object Identifier: 10.1214/15-AOS1350

Primary: 62F35
Secondary: 62F12

Keywords: Catoni’s estimator , empirical risk minimization , heavy-tailed data , robust $k$-means clustering , robust regression

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 6 • December 2015
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