Statistical Inference for Probabilistic Constraint Logic Programming

Most approaches to probabilistic logic programming deal with deduction systems and xpoint semantics for programming systems with user-speci ed weights attached to the formulae of the language, i.e, the aim is to connect logical inference and probabilistic inference. However, such a user-speci c determination of weights is not reusable and often complex. In various applications, automatic methods to estimate weights from empirical data are desirable. This leads to a completely di erent approach to probabilistic logic programming, where the central problem is a speci cation of a probability distribution over the answers of the system and the use of statistical methods to estimate the probabilistic parameters from data. In this paper we present a probabilistic model for constraint logic programming, coupled with an algorithm for statistical inference about the parameters of such probabilistic models from incomplete data. The probability model we use is a powerful log-linear probability distribution over the proof trees that a program yields for a sample of queries. The statistical parameter estimation method we present is an extension of the improved iterative scaling algorithm of Della Pietra, Della Pietra, and La erty (1997) to incomplete data. This extension obviates the need to rely on large samples of analyses of the system for training. In addition, we provide an algorithm for search for most probable proof trees based upon the method of Viterbi (1967). This enables to nd the most probable answer of a query e ciently.