Fast rates for support vector machines using Gaussian kernels

2007/04/01 by Ingo Steinwart, Clint Scovel · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Machine Learning and Algorithms #Statistical Methods and Inference #math.ST #msc:41A46 #msc:41A99 #msc:62G20 #msc:62G99 #msc:68Q32 #msc:68T05 #msc:68T10 #stat.ML #stat.TH

paper · pdf · doi:10.1214/009053606000001226

published as Annals of Statistics 2007, Vol. 35, No. 2, 575-607 · Published at http://dx.doi.org/10.1214/009053606000001226 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2007/04/01 · arxiv created 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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