Discriminative training via linear programming

Abstract

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 piece-wise 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.