PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Error bounds for learning the kernel
Charles Micchelli, Massimiliano Pontil, Qiang WU and Ding-Xuan Zhou
Research Note Number 05/09, pp. 1-14, 2005.

Abstract

The problem of learning the kernel function has recently received considerable attention in machine learning. Much of the work so far has focused on kernel selection criteria, particularly on minimizing a regularized error functional over a prescribed set of kernels. Empirical studies indicate that this approach can enhance statistical performance and is computationally feasible. In this paper, we present a theoretical analysis of its generalization error. We establish for a wide variety of classes of kernels, such as the set of all multivariate Gaussian kernels, that this learning method generalizes well and, when the regularization parameter is appropriately chosen, it is consistent. A central role in our analysis is played by the interaction between the sample error and the approximation error. }

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1014
Deposited By:Massimiliano Pontil
Deposited On:11 July 2005