Learning the Kernel with Hyperkernels

作者：Cheng Soon Ong, Alexander Johannes Smola, Robert C. Williamson, Ralf Herbrich · 发表于：ANU Open Research (Australian National University) · 年份：2003 · 被引用次数：318 · 研究领域：Control Systems and Identification、Gaussian Processes and Bayesian Inference、Fault Detection and Control Systems

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.