CONF grandvalet:nips:2005/IDIAP A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification Grandvalet, Yves Mariéthoz, Johnny Bengio, Samy EXTERNAL https://publications.idiap.ch/attachments/papers/2005/grandvalet-nips-2005.pdf PUBLIC https://publications.idiap.ch/index.php/publications/showcite/grandvalet:rr05-26 Related documents Advances in Neural Information Processing Systems, NIPS 15 2005 IDIAP-RR 05-26 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 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-the-art procedures. REPORT grandvalet:rr05-26/IDIAP A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification Grandvalet, Yves Mariéthoz, Johnny Bengio, Samy EXTERNAL https://publications.idiap.ch/attachments/reports/2005/grandvalet-idiap-rr-05-26.pdf PUBLIC Idiap-RR-26-2005 2005 IDIAP Published in Advances in Neural Information Processing Systems, {NIPS} 15, 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 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-the-art procedures.