424 research outputs found
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
Weakly Restricted Stochastic Grammars
A new type of stochastic grammars is introduced for investigation: weakly restricted stochastic grammars. In this paper we will concentrate on the consistency problem. To find conditions for stochastic grammars to be consistent, the theory of multitype Galton-Watson branching processes and generating functions is of central importance.\ud
The unrestricted stochastic grammar formalism generates the same class of languages as the weakly restricted formalism. The inside-outside algorithm is adapted for use with weakly restricted grammars
Calibrating Generative Models: The Probabilistic Chomsky-SchĆ¼tzenberger Hierarchy
A probabilistic ChomskyāSchĆ¼tzenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning
Data-Oriented Language Processing. An Overview
During the last few years, a new approach to language processing has started
to emerge, which has become known under various labels such as "data-oriented
parsing", "corpus-based interpretation", and "tree-bank grammar" (cf. van den
Berg et al. 1994; Bod 1992-96; Bod et al. 1996a/b; Bonnema 1996; Charniak
1996a/b; Goodman 1996; Kaplan 1996; Rajman 1995a/b; Scha 1990-92; Sekine &
Grishman 1995; Sima'an et al. 1994; Sima'an 1995-96; Tugwell 1995). This
approach, which we will call "data-oriented processing" or "DOP", embodies the
assumption that human language perception and production works with
representations of concrete past language experiences, rather than with
abstract linguistic rules. The models that instantiate this approach therefore
maintain large corpora of linguistic representations of previously occurring
utterances. When processing a new input utterance, analyses of this utterance
are constructed by combining fragments from the corpus; the
occurrence-frequencies of the fragments are used to estimate which analysis is
the most probable one.
In this paper we give an in-depth discussion of a data-oriented processing
model which employs a corpus of labelled phrase-structure trees. Then we review
some other models that instantiate the DOP approach. Many of these models also
employ labelled phrase-structure trees, but use different criteria for
extracting fragments from the corpus or employ different disambiguation
strategies (Bod 1996b; Charniak 1996a/b; Goodman 1996; Rajman 1995a/b; Sekine &
Grishman 1995; Sima'an 1995-96); other models use richer formalisms for their
corpus annotations (van den Berg et al. 1994; Bod et al., 1996a/b; Bonnema
1996; Kaplan 1996; Tugwell 1995).Comment: 34 pages, Postscrip
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