Hyperkernels

We consider the problem of choosing a kernel suitable for estimation using a Gaussian Process estimator or a Support Vector Machine. A novel solution is presented which involves defining a Reproducing Ker- nel Hilbert Space on the space of kernels itself. By utilizing an analog of the classical representer theorem, the problem of choosing a kernel from a parameterized family of kernels (e. g. of varying width) is reduced to a statistical estimation problem akin to the problem of minimizing a regularized risk functional. Various classical settings for model or kernel selection are special cases of our framework.

Authors

• Cheng Ong
• Robert Williamson
• Alex Smola

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