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

Probabilistic Parsing Strategies

We present new results on the relation between purely symbolic context-free parsing strategies and their probabilistic counter-parts. Such parsing strategies are seen as constructions of push-down devices from grammars. We show that preservation of probability distribution is possible under two conditions, viz. the correct-prefix property and the property of strong predictiveness. These results generalize existing results in the literature that were obtained by considering parsing strategies in isolation. From our general results we also derive negative results on so-called generalized LR parsing.Comment: 36 pages, 1 figur

Three New Probabilistic Models for Dependency Parsing: An Exploration

After presenting a novel O(n^3) parsing algorithm for dependency grammar, we develop three contrasting ways to stochasticize it. We propose (a) a lexical affinity model where words struggle to modify each other, (b) a sense tagging model where words fluctuate randomly in their selectional preferences, and (c) a generative model where the speaker fleshes out each word's syntactic and conceptual structure without regard to the implications for the hearer. We also give preliminary empirical results from evaluating the three models' parsing performance on annotated Wall Street Journal training text (derived from the Penn Treebank). In these results, the generative (i.e., top-down) model performs significantly better than the others, and does about equally well at assigning part-of-speech tags.Comment: 6 pages, LaTeX 2.09 packaged with 4 .eps files, also uses colap.sty and acl.bs

Precise n-gram Probabilities from Stochastic Context-free Grammars

We present an algorithm for computing n-gram probabilities from stochastic context-free grammars, a procedure that can alleviate some of the standard problems associated with n-grams (estimation from sparse data, lack of linguistic structure, among others). The method operates via the computation of substring expectations, which in turn is accomplished by solving systems of linear equations derived from the grammar. We discuss efficient implementation of the algorithm and report our practical experience with it.Comment: 12 pages, to appear in ACL-9

Efficient Algorithms for Parsing the DOP Model

Excellent results have been reported for Data-Oriented Parsing (DOP) of natural language texts (Bod, 1993). Unfortunately, existing algorithms are both computationally intensive and difficult to implement. Previous algorithms are expensive due to two factors: the exponential number of rules that must be generated and the use of a Monte Carlo parsing algorithm. In this paper we solve the first problem by a novel reduction of the DOP model to a small, equivalent probabilistic context-free grammar. We solve the second problem by a novel deterministic parsing strategy that maximizes the expected number of correct constituents, rather than the probability of a correct parse tree. Using the optimizations, experiments yield a 97% crossing brackets rate and 88% zero crossing brackets rate. This differs significantly from the results reported by Bod, and is comparable to results from a duplication of Pereira and Schabes's (1992) experiment on the same data. We show that Bod's results are at least partially due to an extremely fortuitous choice of test data, and partially due to using cleaner data than other researchers.Comment: 10 page

Measuring efficiency in high-accuracy, broad-coverage statistical parsing

Very little attention has been paid to the comparison of efficiency between high accuracy statistical parsers. This paper proposes one machine-independent metric that is general enough to allow comparisons across very different parsing architectures. This metric, which we call ``events considered'', measures the number of ``events'', however they are defined for a particular parser, for which a probability must be calculated, in order to find the parse. It is applicable to single-pass or multi-stage parsers. We discuss the advantages of the metric, and demonstrate its usefulness by using it to compare two parsers which differ in several fundamental ways.Comment: 8 pages, 4 figures, 2 table