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@TECHREPORT{grandvalet:rr05-26,
                      author = {Grandvalet, Yves and Mari{\'{e}}thoz, Johnny and Bengio, Samy},
                    projects = {Idiap},
                       title = {A Probabilistic Interpretation of SVMs with an Application to Unbalanced Classification},
                        type = {Idiap-RR},
                      number = {Idiap-RR-26-2005},
                        year = {2005},
                 institution = {IDIAP},
                        note = {Published in Advances in Neural Information Processing Systems, {NIPS} 15, 2005},
                    abstract = {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.},
                         pdf = {https://publications.idiap.ch/attachments/reports/2005/grandvalet-idiap-rr-05-26.pdf},
                  postscript = {ftp://ftp.idiap.ch/pub/reports/2005/grandvalet-idiap-rr-05-26.ps.gz},
ipdmembership={learning},
}