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Zbl 1127.68091
Steinwart, Ingo; Scovel, Clint
Fast rates for support vector machines using Gaussian kernels. (English)
[J] Ann. Stat. 35, No. 2, 575-607 (2007). ISSN 0090-5364

Summary: For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines 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.

MSC 2000:: *68T05 Learning and adaptive systems
68Q32 Computational learning theory
62G20 Nonparametric asymptotic efficiency
68T10 Pattern recognition
41A46 Approximation by arbitrary nonlinear expressions

Keywords: support vector machines; classification; nonlinear discrimination; learning rates; noise assumption; Gaussian RBF kernels

Cited in: Zbl 1209.62146

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