When do support vector machines work fast?
- Ingo
The authors establish learning rates to the Bayes risk for support vector machines (SVM's) with hinge loss. Since a theorem of Devroyte states that no learning algorithm can learn with a uniform rate to the Bayes risk for all probability distributions they have to restrict the class of considered distributions: in order to obtain fast rates they assume a noise condition recently proposed by Tsybakov and an approximation condition in terms of the distribution and the reproducing kernel Hilbert space used by the SVM. for Gaussian RBF kernels with varying widths they propose a geometric noise assumption on the distribution which ensures the approximation condition. This geometric assumption is not in terms of smoothness but describes the concentration of the marginal distribution near the decision boundary. In particular they are able to describe nontrivial classes of distributions for which SVM's using a Gaussian kernel can learn with almost linear rate.
- Research Organization:
- Los Alamos National Laboratory
- Sponsoring Organization:
- DOE
- OSTI ID:
- 977540
- Report Number(s):
- LA-UR-04-2391
- Country of Publication:
- United States
- Language:
- English
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