Institute of Mathematical Statistics Lecture Notes - Monograph Series

A new concentration result for regularized risk minimizers

Don Hush, Clint Scovel, and Ingo Steinwart

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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 $\a=2$.

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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

First available in Project Euclid: 28 November 2007

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Copyright © 2006, Institute of Mathematical Statistics


Steinwart, Ingo; Hush, Don; Scovel, Clint. A new concentration result for regularized risk minimizers. High Dimensional Probability, 260--275, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000897.

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