PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning convex combinations of continuously parameterized basic kernels
Andreas Argyriou, Charles A. Micchelli and Massimiliano Pontil
Lecture Notes in Computer Science. Learning Theory: 18th Annual Conference on Learning Theory, COLT 2005, Bertinoro, Italy, June 27-30, 2005. Proceedings Volume 3559, pp. 338-352, 2005. ISSN 0302-9743

Abstract

We study the problem of learning a kernel which minimizes a regularization error functional such as that used in regularization networks or support vector machines. We consider this problem when the kernel is in the convex hull of basic kernels, for example, Gaussian kernels which are continuously parameterized by a compact set. We show that there always exists an optimal kernel which is the convex combination of at most m+1 basic kernels, where m is the sample size, and provide a necessary and sufficient condition for a kernel to be optimal. The proof of our results is constructive and leads to a greedy algorithm for learning the kernel. We discuss the properties of this algorithm and present some preliminary numerical simulations.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:1170
Deposited By:Andreas Argyriou
Deposited On:19 November 2005