Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Conference Paper

Entropy numbers, operators and support vector kernels

There are no MPG-Authors in the publication available
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

Williamson, R., Smola, A., & Schölkopf, B. (1999). Entropy numbers, operators and support vector kernels. In R. Fischer, & H. Simon (Eds.), Computational Learning Theory: 4th European Conference, EuroCOLT’99 Nordkirchen, Germany, March 29–31, 1999 (pp. 285-299). Berlin, Germany: Springer.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-E759-5
We derive new bounds for the generalization error of feature space machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs are based on a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinite dimensional unit ball in feature space into a finite dimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator, can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence we are able to theoretically explain the effect of the choice of kernel functions on the generalization performance of support vector machines.