Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs

Gretton, A; Herbrich R, Schölkopf, B; Rayner, PJW

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Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs

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Gretton, A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Herbrich R, Schölkopf, B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Gretton, A., Herbrich R, Schölkopf, B., & Rayner, P.(2001). Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E39A-4

Abstract

Three estimates of the leave-one-out error for nu-support vector (SV) machine binary classifiers are presented. Two of the estimates are based on the geometrical concept of the em span, which was introduced in the context of bounding the leave-one-out error for C-SV machine binary classifiers, while the third is based on optimisation over the criterion used to train the nu-support vector classifier. It is shown that the estimates presented herein provide informative and efficient approximations of the generalisation behaviour, in both a toy example and benchmark data sets. The proof strategies in the nu-SV context are also compared with those used to derive leave-one-out error estimates in the C-SV case.