Discriminative Learning for Probabilistic Context-Free Grammars based on Generalized H-Criterion

We present a formal framework for the development of a family of discriminative learning algorithms for Probabilistic Context-Free Grammars (PCFGs) based on a generalization of criterion-H. First of all, we propose the H-criterion as the objective function and the Growth Transformations as the optimization method, which allows us to develop the final expressions for the estimation of the parameters of the PCFGs. And second, we generalize the H-criterion to take into account the set of reference interpretations and the set of competing interpretations, and we propose a new family of objective functions that allow us to develop the expressions of the estimation transformations for PCFGs.