PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning the kernel function via regularization
Massimiliano Pontil and Charles Micchelli
(2004) Technical Report. UCL, UK.

Abstract

We study the problem of finding an optimal kernel from a prescribed convex set of kernels $\calK$ for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although $\calK$ may be an uncountable set, the optimal kernel is always obtained as a convex combination of at most $m+1$ kernels, where $m$ is the number of data examples. In particular, our results apply to learning the optimal radial kernel or the optimal dot product kernel.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:455
Deposited By:Massimiliano Pontil
Deposited On:23 December 2004