Type-based MCMC for Sampling Tree Fragments from Forests

This paper applies type-based Markov Chain Monte Carlo (MCMC) algorithms to the problem of learning Synchronous Context-Free Grammar (SCFG) rules from a forest that represents all possible rules consistent with a fixed word alignment. While type-based MCMC has been shown to be effective in a number of NLP applications, our setting, where the tree structure of the sentence is itself a hidden variable, presents a number of challenges to type-based inference. We describe methods for defining variable types and efficiently indexing variables in order to overcome these challenges. These methods lead to improvements in both log likelihood and BLEU score in our experiments.