Fast rates for support vector machines using Gaussian kernels

The Annals of Statistics · 2007 · Volume 35 · Issue 2

Abstract

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.

Keywords

41A46, 41A99, 62G20, 62G99, 68Q32, 68T05, 68T10, ‎classification‎, Gaussian RBF kernels, learning rates, noise assumption, nonlinear discrimination, Support vector machines

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