The Annals of Statistics
- Ann. Statist.
- Volume 43, Number 6 (2015), 2507-2536.
Empirical risk minimization for heavy-tailed losses
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.
Ann. Statist. Volume 43, Number 6 (2015), 2507-2536.
Received: June 2014
Revised: May 2015
First available in Project Euclid: 7 October 2015
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Brownlees, Christian; Joly, Emilien; Lugosi, Gábor. Empirical risk minimization for heavy-tailed losses. Ann. Statist. 43 (2015), no. 6, 2507--2536. doi:10.1214/15-AOS1350. http://projecteuclid.org/euclid.aos/1444222083.