An Efficient Probabilistic Context-Free Parsing Algorithm that Computes Prefix Probabilities

We describe an extension of Earley's parser for stochastic context-free grammars that computes the following quantities given a stochastic context-free grammar and an input string: a) probabilities of successive prefixes being generated by the grammar; b) probabilities of substrings being generated by the nonterminals, including the entire string being generated by the grammar; c) most likely (Viterbi) parse of the string; d) posterior expected number of applications of each grammar production, as required for reestimating rule probabilities. (a) and (b) are computed incrementally in a single left-to-right pass over the input. Our algorithm compares favorably to standard bottom-up parsing methods for SCFGs in that it works efficiently on sparse grammars by making use of Earley's top-down control structure. It can process any context-free rule format without conversion to some normal form, and combines computations for (a) through (d) in a single algorithm. Finally, the algorithm has simple extensions for processing partially bracketed inputs, and for finding partial parses and their likelihoods on ungrammatical inputs.Comment: 45 pages. Slightly shortened version to appear in Computational Linguistics 2

Edge-Based Best-First Chart Parsing

Best-first probabilistic chart parsing attempts to parse efficiently by working on edges that are judged 'best' by some probabilistic figure of merit (FOM). Recent work has used proba- bilistic context-free grammars (PCFGs) to sign probabilities to constituents, and to use these probabilities as the starting point for the FOM. This paper extends this approach to us- ing a probabilistic FOM to judge edges (incomplete constituents), thereby giving a much finergrained control over parsing effort. We show how this can be accomplished in a particularly simple way using the common idea of binarizing the PCFG. The results obtained are about a factor of twenty improvement over the best prior results -- that is, our parser achieves equivalent results using one twentieth the number of edges. Furthermore we show that this improvement is obtained with parsing precision and recall levels superior to those achieved by exhaustive parsing