Factored A* Search for Models over Sequences and Trees

We investigate the calculation of A* bounds for sequence and tree models which are the explicit intersection of a set of simpler models or can be bounded by such an intersection. We provide a natural viewpoint which unifies various instances of factored A* models for trees and sequences, some previously known and others novel, including multiple sequence alignment, weighted finite-state transducer composition, and lexicalized statistical parsing. The specific case of parsing with a product of syntactic (PCFG) and semantic (lexical dependency) components is then considered in detail. We show that this factorization gives a modular lexicalized parser which is simpler than comparably accurate non-factored models, and which allows efficient exact inference with large treebank grammars.