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

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

Analyzing and Improving Statistical Language Models for Speech Recognition

In many current speech recognizers, a statistical language model is used to indicate how likely it is that a certain word will be spoken next, given the words recognized so far. How can statistical language models be improved so that more complex speech recognition tasks can be tackled? Since the knowledge of the weaknesses of any theory often makes improving the theory easier, the central idea of this thesis is to analyze the weaknesses of existing statistical language models in order to subsequently improve them. To that end, we formally define a weakness of a statistical language model in terms of the logarithm of the total probability, LTP, a term closely related to the standard perplexity measure used to evaluate statistical language models. We apply our definition of a weakness to a frequently used statistical language model, called a bi-pos model. This results, for example, in a new modeling of unknown words which improves the performance of the model by 14% to 21%. Moreover, one of the identified weaknesses has prompted the development of our generalized N-pos language model, which is also outlined in this thesis. It can incorporate linguistic knowledge even if it extends over many words and this is not feasible in a traditional N-pos model. This leads to a discussion of whatknowledge should be added to statistical language models in general and we give criteria for selecting potentially useful knowledge. These results show the usefulness of both our definition of a weakness and of performing an analysis of weaknesses of statistical language models in general.Comment: 140 pages, postscript, approx 500KB, if problems with delivery, mail to [email protected]

Computation of Probabilities for an Island-Driven Parser

The authors describe an effort to adapt island-driven parsers to handle stochastic context-free grammars. These grammars could be used as language models (LMs) by a language processor (LP) to computer the probability of a linguistic interpretation. As different islands may compete for growth, it is important to compute the probability that an LM generates a sentence containing islands and gaps between them. Algorithms for computing these probabilities are introduced. The complexity of these algorithms is analyzed both from theoretical and practical points of view. It is shown that the computation of probabilities in the presence of gaps of unknown length requires the impractical solution of a nonlinear system of equations, whereas the computation of probabilities for cases with gaps containing a known number of unknown words has polynomial time complexity and is practically feasible. The use of the results obtained in automatic speech understanding systems is discussed