A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

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Yves Grandvalet, Johnny Mariethoz, Samy Bengio


In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation pro- cedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the sug- gested mapping is interval-valued, providing a set of posterior probabil- ities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classifica- tion, when decisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.