First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs

TL;DR

This paper introduces DC#, a hybrid probabilistic logic programming language that models various independencies and presents FO-CS-LW, a scalable inference algorithm extending context-specific likelihood weighting to first-order logic.

Contribution

It proposes DC#, integrating three types of independencies in hybrid models, and develops FO-CS-LW, a novel scalable inference algorithm for first-order probabilistic logic programs.

Findings

DC# effectively models multiple types of independencies.

FO-CS-LW scales inference in hybrid probabilistic logic programs.

The approach improves inference efficiency in complex relational models.

Abstract

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with unification and combining rules to the first-order case.