We propose an efficient discriminative training method for generative models under supervised learning. In our setting, fully observed instances are given as training examples, together with a specification of variables of interest for prediction. We formulate the training as a convex programming problem, incorporating the SVM-type large margin constraints to favor parameters under which the maximum a posteriori (MAP) estimates of the prediction variables, conditioned on the rest, are close to their true values given in the training instances. The resulting optimization problem is, however, more complex than its quadratic programming (QP) counterpart resulting from the SVM-type training of conditional models, because of the presence of non-linear constraints on the parameters. We present an efficient optimization method, which combines several techniques, namely, a data-dependent reparametrization of dual variables, restricted simplicial decomposition, and the proximal point algorithm. Our method extends the one for solving the aforementioned QP counterpart, proposed earlier by some of the authors
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