On the Independencies Hidden in the Structure of a Probabilistic Logic Program

TL;DR

This paper extends the concept of d-separation to probabilistic logic programs, providing a method to infer conditional independencies in non-ground programs with improved computational efficiency.

Contribution

It generalizes d-separation reasoning to non-ground probabilistic logic programs and introduces a meta-interpreter for efficient independence inference.

Findings

Meta-interpreter outperforms exact inference in ProbLog 2

Provides a correctness proof for independence inference

Identifies a fragment of program structures with complete inference capabilities

Abstract

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs correspond to Bayesian networks on their dependency graph, we can compute conditional independencies from d-separation in the latter. In the present paper, we generalize the reasoning above to the non-ground case. First, we abstract the notion of a probabilistic logic program away from external databases and probabilities to obtain so-called program structures. We then present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure on a given external database. Finally, we give a fragment of program structures for which we obtain a completeness statement of our conditional independence oracle. We close with an experimental evaluation of our approach revealing that our meta-interpreter performs significantly faster than checking the definition of independence using exact inference in ProbLog 2.