Fast rates for support vector machines using Gaussian kernels

Details Fast rates for support vector machines using Gaussian kernels Fast rates for support vector machines using Gaussian kernels

2007-08-14

arxiv.org/abs/0708.1838v1

Annals of Statistics 2007, Vol. 35, No. 2, 575-607

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001226 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001226

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometric noise condition which is used to bound the approximation error. Unlike previously proposed concepts for bounding the approximation error, the geometric noise assumption does not employ any smoothness assumption.

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