First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs
This work addresses the problem of scalable inference in hybrid probabilistic logic programs for researchers in statistical relational AI, though it is incremental as it builds on existing methods like CS-LW.
The paper tackles the challenge of efficient inference in hybrid probabilistic models by introducing DC#, a language that integrates distributional clauses with Bayesian logic programming principles, and FO-CS-LW, a scalable sampling algorithm that extends context-specific likelihood weighting to first-order cases, achieving improved inference efficiency as demonstrated in experiments.
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.