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Conference Paper

On the Complexity of Learning the Kernel Matrix

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83967

Herrmann,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Bousquet, O., & Herrmann, D. (2003). On the Complexity of Learning the Kernel Matrix. Advances in Neural Information Processing Systems, 15, 399-406.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-DB4B-4
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.