Lifted Variable Elimination for Probabilistic Logic Programming
This work addresses the challenge of efficient inference in probabilistic logic programming for AI and machine learning applications, though it is incremental as it adapts existing lifted inference techniques to a new framework.
The paper tackled the problem of performing lifted inference for probabilistic logic programming (PLP) to compute query probabilities efficiently based on domain sizes rather than instances, by adapting Generalized Counting First Order Variable Elimination (GC-FOVE) to PLP and extending the Prolog Factor Language with new factors and operators, resulting in the LP^2 algorithm that showed potential in benchmarks compared to existing methods like PITA and ProbLog2.
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.