A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification

In this paper, we show that the hinge loss can be interpreted as the neglog-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semiparametric model fitted by a maximum a posteriori estimation procedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mapping is interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem when decisions result in unequal losses. Experiments on an unbalanced classification loss show improvements over state-of-theart procedures.