How Implicit Negative Evidence Improve Weighted Context-Free Grammar Induction

Probabilistic context-free grammars (PCFGs) or in general a weighted context-free grammars (WCFGs) are widely used in many areas of syntactic pattern matching, especially in statistical natural language parsing or biological modeling. For a given a fixed set of context-free grammar rules, probabilities of its rules can be estimated by using the Inside-Outside algorithm (IO), which is a special case of an expectation-maximization method. The IO algorithm implies only positive examples in the data given. In this paper a modified IO algorithm to estimate probabilistic parameters over implicit positive and also negative evidence is proposed. We demonstrate that a Contrastive Estimation based method outperforms a standard IO algorithm in terms of Precision, without any loss of Recall.