Support vector machines with a reject option

Yves Grandvalet, Alain Rakotomamonjy, Joseph Keshet, Stéphane Canu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

89 Scopus citations

Abstract

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently. We finally provide preliminary experimental results illustrating the interest of our constructive approach to devising loss functions.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
PublisherNeural Information Processing Systems
Pages537-544
Number of pages8
ISBN (Print)9781605609492
StatePublished - 2009
Externally publishedYes
Event22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada
Duration: 8 Dec 200811 Dec 2008

Publication series

NameAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

Conference

Conference22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
Country/TerritoryCanada
CityVancouver, BC
Period8/12/0811/12/08

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