We establish learning rates up to the order of $n^{-1}$ for support vector machines with hinge loss (L1-SVMs) and nontrivial distributions. For the stochastic analysis of these algorithms we use recently developed concepts such as Tsybakov's noise assumption and local Rademacher averages. Furthermore we introduce a new geometric noise condition for distributions that is used to bound the approximation error of Gaussian kernels in terms of their widths.
I. Steinwart and C. Scovel, Fast Rates for Support Vector Machines using Gaussian Kernels. Annals of Statistics, Vol. 35, pp. 575-607, 2007. Los Alamos National Laboratory Technical Report LA-UR-04-8796. [ Abstract | PDF (403 KB) ]
