Fast rates for support vector machines using gaussian kernels'

• 成果类型: Article
• 署名作者: Steinwart, Ingo; Scovel, Clint
• 署名单位: United States Department of Energy (DOE); Los Alamos National Laboratory
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001226
• 发表日期: 2007
• 页码: 575-607
• 关键词: Empirical Processes; Concentration inequalities; CLASSIFICATION; Consistency; RISK; DISCRIMINATION; CONVERGENCE; CLASSIFIERS; SPACES; bounds

摘要

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.