Bayesian network models are widely used for discriminative prediction tasks such as classification. Usually their parameters are determined using ‘unsupervised’ methods such as maximization of the joint likelihood. The reason is often that it is unclear how to find the parameters maximizing the conditional (supervised) likelihood. We show how the discriminative learning problem can be solved efficiently for a large class of Bayesian network models, including the Naive Bayes (NB) and treeaugmented Naive Bayes (TAN) models. We do this by showing that under a certain general condition on the network structure, the discriminative learning problem is exactly equivalent to logistic regression with unconstrained convex parameter spaces. Hitherto this was known only for Naive Bayes models. Since logistic regression models have a concave log-likelihood surface, the global maximum can be easily found by local optimization methods.

This paper presents a linear programming approach to discriminative training. We first define a measure of discrimination of an arbitrary conditional probability model on a set of labeled training data. We consider maximizing discrimination on a parametric family of exponential models that arises naturally in the maximum entropy framework. We show that this optimization problem is globally convex in Rⁿ, and is moreover piecewise linear on Rⁿ. We propose a solution that involves solving a series of linear programming problems. We provide a characterization of global optimizers. We compare this framework with those of minimum classification error and maximum entropy

Discriminative models have been of interest in the NLP community in recent years.