7,268 research outputs found
Probabilistic Constraint Logic Programming
This paper addresses two central problems for probabilistic processing
models: parameter estimation from incomplete data and efficient retrieval of
most probable analyses. These questions have been answered satisfactorily only
for probabilistic regular and context-free models. We address these problems
for a more expressive probabilistic constraint logic programming model. We
present a log-linear probability model for probabilistic constraint logic
programming. On top of this model we define an algorithm to estimate the
parameters and to select the properties of log-linear models from incomplete
data. This algorithm is an extension of the improved iterative scaling
algorithm of Della-Pietra, Della-Pietra, and Lafferty (1995). Our algorithm
applies to log-linear models in general and is accompanied with suitable
approximation methods when applied to large data spaces. Furthermore, we
present an approach for searching for most probable analyses of the
probabilistic constraint logic programming model. This method can be applied to
the ambiguity resolution problem in natural language processing applications.Comment: 35 pages, uses sfbart.cl
Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning
Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate
A Tutorial on the Expectation-Maximization Algorithm Including Maximum-Likelihood Estimation and EM Training of Probabilistic Context-Free Grammars
The paper gives a brief review of the expectation-maximization algorithm
(Dempster 1977) in the comprehensible framework of discrete mathematics. In
Section 2, two prominent estimation methods, the relative-frequency estimation
and the maximum-likelihood estimation are presented. Section 3 is dedicated to
the expectation-maximization algorithm and a simpler variant, the generalized
expectation-maximization algorithm. In Section 4, two loaded dice are rolled. A
more interesting example is presented in Section 5: The estimation of
probabilistic context-free grammars.Comment: Presented at the 15th European Summer School in Logic, Language and
Information (ESSLLI 2003). Example 5 extended (and partially corrected
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
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
Stochastic Attribute-Value Grammars
Probabilistic analogues of regular and context-free grammars are well-known
in computational linguistics, and currently the subject of intensive research.
To date, however, no satisfactory probabilistic analogue of attribute-value
grammars has been proposed: previous attempts have failed to define a correct
parameter-estimation algorithm.
In the present paper, I define stochastic attribute-value grammars and give a
correct algorithm for estimating their parameters. The estimation algorithm is
adapted from Della Pietra, Della Pietra, and Lafferty (1995). To estimate model
parameters, it is necessary to compute the expectations of certain functions
under random fields. In the application discussed by Della Pietra, Della
Pietra, and Lafferty (representing English orthographic constraints), Gibbs
sampling can be used to estimate the needed expectations. The fact that
attribute-value grammars generate constrained languages makes Gibbs sampling
inapplicable, but I show how a variant of Gibbs sampling, the
Metropolis-Hastings algorithm, can be used instead.Comment: 23 pages, 21 Postscript figures, uses rotate.st
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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