On the Influence of the Kernel on the Consistency of Support Vector Machines

by Ingo Stainwart

This is kind of math paper. I haven't really delved into some mathematical stuffs for a long time.This paper might be the first to explore the consistency of SVM (that is the asymptotic behavior of the classifier compared with the optimal, Bayes decision error). The main result might be as follows:
For universal kernels we have consistency result for L2 and L1 soft margin classifiers.
The universal kernels are those whose induced RKHS is dense in continuous function space. Gaussian and Laplacian kernels are both universal. The author derived the corresponding consistency.
At first glance I thought they find some tricks in choosing regularization parameters. But I didn't find anything truely usable (e.g. corollary 18).

The editor is Scholkopf... I guess only huge bulls like him understands the key points. For now I just have quite a faint idea.