PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Support Vector Machines with a Reject Option
Yves Grandvalet, Alain Rakotomamonjy, Joseph Keshet and Stéphane Canu
In: NIPS 21, Dec 2008, Vancouver, Canada.


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.

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EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:4715
Deposited By:Yves Grandvalet
Deposited On:24 March 2009