A new concentration result for regularized risk minimizers

Details A new concentration result for regularized risk minimizers A new concentration result for regularized risk minimizers

2006-12-27

arxiv.org/abs/math/0612779v1

IMS Lecture Notes Monograph Series 2006, Vol. 51, 260-275

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000897 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000897

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 $L_{\alpha}(y,t)=|y-t|^{\alpha}$ with $\alpha$ near 1 may often be preferable to the usual choice of $\alpha=2$.

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