A note on extending generalization bounds for binary large-margin classifiers to multiple classes

  • Authors:
  • Ürün Dogan;Tobias Glasmachers;Christian Igel

  • Affiliations:
  • Institut für Mathematik, Universität Potsdam, Germany;Institut für Neuroinformatik, Ruhr-Universität Bochum, Germany;Department of Computer Science, University of Copenhagen, Denmark

  • Venue:
  • ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
  • Year:
  • 2012

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Abstract

A generic way to extend generalization bounds for binary large-margin classifiers to large-margin multi-category classifiers is presented. The simple proceeding leads to surprisingly tight bounds showing the same $\tilde{O}(d^2)$ scaling in the number d of classes as state-of-the-art results. The approach is exemplified by extending a textbook bound based on Rademacher complexity, which leads to a multi-class bound depending on the sum of the margin violations of the classifier.