Our main contribution lies in the novel integration of existing techniques and algorithms in parsing and grammar induction to offer a complete solution for simultaneously modeling grounded language at the sentence and discourse levels.
we: (1) use the Earley algorithm to exploit the special structure of our grammars, which are deterministic or have at most bounded ambiguity, to achieve approximately linear parsing time; (2) suggest a rescaling approach that enables us to build a PCFG parser capable of handling very long strings with thousands of tokens; and (3) employ Variational Bayes for grammatical inference to obtain better grammars than those given by the EM algorithm.