Institute of Mathematical Statistics Lecture Notes - Monograph Series

A new concentration result for regularized risk minimizers

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 $\a=2$.

Chapter information

Source
Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn, eds., High Dimensional Probability: Proceedings of the Fourth International Conference (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 260-275

Dates
First available in Project Euclid: 28 November 2007

https://projecteuclid.org/euclid.lnms/1196284117

Digital Object Identifier
doi:10.1214/074921706000000897

Mathematical Reviews number (MathSciNet)
MR2387774

Zentralblatt MATH identifier
1127.68090

Rights