The Annals of Statistics

Fast rates for support vector machines using Gaussian kernels

Ingo Steinwart and Clint Scovel

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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.

Article information

Ann. Statist., Volume 35, Number 2 (2007), 575-607.

First available in Project Euclid: 5 July 2007

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Zentralblatt MATH identifier

Primary: 68Q32: Computational learning theory [See also 68T05]
Secondary: 62G20: Asymptotic properties 62G99: None of the above, but in this section 68T05: Learning and adaptive systems [See also 68Q32, 91E40] 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30} 41A46: Approximation by arbitrary nonlinear expressions; widths and entropy 41A99: None of the above, but in this section

Support vector machines classification nonlinear discrimination learning rates noise assumption Gaussian RBF kernels


Steinwart, Ingo; Scovel, Clint. Fast rates for support vector machines using Gaussian kernels. Ann. Statist. 35 (2007), no. 2, 575--607. doi:10.1214/009053606000001226.

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