Sampling Tree Fragments from Forests

We study the problem of sampling trees from forests, in the setting where probabilities for each tree may be a function of arbitrarily large tree fragments. This setting extends recent work for sampling to learn Tree Substitution Grammars to the case where the tree structure TSG derived tree is not fixed. We develop a Markov chain Monte Carlo algorithm which corrects for the bias introduced by unbalanced forests, and we present experiments using the algorithm to learn Synchronous Context-Free Grammar rules for machine translation. In this application, the forests being sampled represent the set of Hiero-style rules that are consistent with fixed input word-level alignments. We demonstrate equivalent machine translation performance to standard techniques but with much smaller grammars.