Constraint-Based Inference in Probabilistic Logic Programs

TL;DR

This paper introduces Ordered Symbolic Derivation Diagrams (OSDDs), a new data structure for probabilistic logic programs that enables more efficient exact and approximate inference by leveraging constraint formulas.

Contribution

The paper proposes OSDDs and a program transformation technique for constructing them, improving inference efficiency in probabilistic logic programming.

Findings

OSDDs enable more compact representation of possible worlds.

Exact inference with OSDDs can be faster than traditional methods.

Approximate inference with OSDDs reduces rejection rate and variance.

Abstract

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query in a suitable data structure, and using it to compute the answer probability. Systems such as ProbLog, PITA, etc., use propositional data structures like explanation graphs, BDDs, SDDs, etc., to represent the possible worlds. While this approach saves inference time due to substructure sharing, there are a number of problems where a more compact data structure is possible. We propose a data structure called Ordered Symbolic Derivation Diagram (OSDD) which captures the possible worlds by means of constraint formulas. We describe a program transformation technique to construct OSDDs via query evaluation, and give procedures to perform exact and approximate inference over OSDDs. Our approach has two key properties. Firstly, the exact inference procedure is a generalization of traditional inference, and results in speedup over the latter in certain settings. Secondly, the approximate technique is a generalization of likelihood weighting in Bayesian Networks, and allows us to perform sampling-based inference with lower rejection rate and variance. We evaluate the effectiveness of the proposed techniques through experiments on several problems. This paper is under consideration for acceptance in TPLP.