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 $\alpha=2$.
I. Steinwart, D. Hush, and C. Scovel, A new Concentration Result for Regularized Risk Minimizers. High-dimensional Probability IV, in IMS Lecture Notes--Monograph Series, Vol. 51, pp. 260-275, 2006. Los Alamos National Laboratory Technical Report LA-UR-05-9403, 2005. [ Abstract | PDF (253 KB) ]
