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Learning the Kernel with Hyperkernels

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Ong,  CS
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Ong, C., Smola, A., & Williamson, R. (2005). Learning the Kernel with Hyperkernels. The Journal of Machine Learning Research, 6, 1043-1071.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D50B-4
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 machine learning problems. Experimental results for classification, regression and novelty detection on UCI data show the feasibility of our approach.