Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger 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

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

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Probabilistic parsing

Postprin

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 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