Learning the Kernel with Hyperkernels

Abstract

This paper addresses the problem of choosing a kernel suitable for estimation with a support
\nvector machine, hence further automating machine learning. This goal is achieved by defining
\na reproducing kernel Hilbert space on the space of kernels itself. Such a formulation leads to a
\nstatistical estimation problem similar to the problem of minimizing a regularized risk functional.
\nWe state the equivalent representer theorem for the choice of kernels and present a semidefinite
\nprogramming formulation of the resulting optimization problem. Several recipes for constructing
\nhyperkernels are provided, as well as the details of common machine learning problems. Experimental
\nresults for classification, regression and novelty detection on UCI data show the feasibility
\nof our approach.