Learning the Kernel with Hyperkernels
Cheng Soon Ong, Alex Smola and Bob Williamson
Journal of Machine Learning Research Volume 6, pp. 1045-1071, 2005.

Abstract

This paper addresses the problem of choosing a kernel suitable for estimation with a Support Vector Machine, hence further automating machine learning. This goal is achieved by defining a Reproducing Kernel Hilbert Space on the space of kernels itself. Such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional. We state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem. Several recipes for constructing hyperkernels are provided, as well as the details of common ma- chine learning problems. Experimental results for classification, regression and novelty detection on UCI data show the feasibility of our approach.

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