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VOL. 51 | 2006 A new concentration result for regularized risk minimizers
Don Hush, Clint Scovel, Ingo Steinwart

Editor(s) Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn

## Abstract

We establish a new concentration result for regularized risk minimizers which is similar to an oracle inequality. Applying this inequality to regularized least squares minimizers like least squares support vector machines, we show that these algorithms learn with (almost) the optimal rate in some specific situations. In addition, for regression our results suggest that using the loss function $L_{\a}(y,t)=|y -t|^{\a}$ with $\a$ near $1$ may often be preferable to the usual choice of $\a=2$.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1127.68090
MathSciNet: MR2387774

Digital Object Identifier: 10.1214/074921706000000897