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Bound on the Leave-One-Out Error for 2-Class Classification using $nu$-{SVM}s


Technical Report


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.

Author(s): Gretton, A. and Herbrich, R. and Schölkopf, B. and Rayner, PJW.
Year: 2001
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: University of Cambridge

Digital: 0
Note: Updated May 2003 (literature review expanded)
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PostScript


  title = {Bound on the Leave-One-Out Error for 2-Class Classification using $nu$-{SVM}s},
  author = {Gretton, A. and Herbrich, R. and Sch{\"o}lkopf, B. and Rayner, PJW.},
  organization = {Max-Planck-Gesellschaft},
  institution = {University of Cambridge},
  school = {Biologische Kybernetik},
  year = {2001},
  note = {Updated May 2003 (literature review expanded)}