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  On the Complexity of Learning the Kernel Matrix

Bousquet, O., & Herrmann, D. (2003). On the Complexity of Learning the Kernel Matrix. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in Neural Information Processing Systems 15 (pp. 399-406). Cambridge, MA, USA: MIT Press.

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 Creators:
Bousquet, O1, 2, Author              
Herrmann, DJL1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We investigate data based procedures for selecting the kernel when learning with Support Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a logarithmic factor bigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting. We thus propose a suitable way of constraining the class. We use an efficient algorithm to solve the resulting optimization problem, present preliminary experimental results, and compare them to an alignment-based approach.

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 Dates: 2003-09
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 1999
 Degree: -

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Title: Sixteenth Annual Conference on Neural Information Processing Systems (NIPS 2002)
Place of Event: Vancouver, Canada
Start-/End Date: 2002-12-09 - 2002-12-14

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Title: Advances in Neural Information Processing Systems 15
Source Genre: Proceedings
 Creator(s):
Becker, S, Editor
Thrun, S, Editor
Obermayer, K, Editor
Affiliations:
-
Publ. Info: Cambridge, MA, USA : MIT Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 399 - 406 Identifier: ISBN: 0-262-02550-7