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