TY - GEN
T1 - Support vector machines with a reject option
AU - Grandvalet, Yves
AU - Rakotomamonjy, Alain
AU - Keshet, Joseph
AU - Canu, Stéphane
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70049110659&partnerID=8YFLogxK
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AN - SCOPUS:70049110659
SN - 9781605609492
T3 - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
SP - 537
EP - 544
BT - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
PB - Neural Information Processing Systems
T2 - 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
Y2 - 8 December 2008 through 11 December 2008
ER -