PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Generalization Bounds for Learning the Kernel
Yiming Ying and Colin Campbell
Techinical Report, University of Bristol (COLT 2009) 2009.

Abstract

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning algorithms reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher chaos complexity by well-established metric entropy integrals and pseudo-dimension of the set of candidate kernels. Our new methodology mainly depends on the principal theory of U-processes. Finally, we establish satisfactory excess generalization bounds and misclassification error rates for learning Gaussian kernels and general radial basis kernels.

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EPrint Type:Article
Additional Information:This is an extension of the COLT paper.
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4263
Deposited By:Yiming Ying
Deposited On:01 February 2009