Lifted Variable Elimination for Probabilistic Logic Programming

TL;DR

This paper introduces LP$^2$, a lifted inference algorithm for probabilistic logic programming that extends existing methods to handle causal independence and heterogeneous factors, improving inference efficiency.

Contribution

It adapts GC-FOVE for probabilistic logic programming, extending PFL with new factors and operators, and demonstrates its effectiveness through implementation and benchmarking.

Findings

LP$^2$ efficiently computes query probabilities in probabilistic logic programs.

The extended algorithm outperforms PITA and ProbLog2 on benchmark tests.

Incorporates causal independence and heterogeneous factors into lifted inference.

Abstract

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP$^2$ for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.