A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification
Yves Grandvalet, Johnny Mariéthoz and Samy Bengio
In: Advances in Neural Information Processing Systems, NIPS, Vancouver, Canada(2005).
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 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
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