Compacting Boolean Formulae for Inference in Probabilistic Logic Programming

Abstract

Knowledge compilation converts Boolean formulae for which some inference tasks are computationally expensive into a representation where the same tasks are tractable. ProbLog is a state-of-the-art Probabilistic Logic Programming system that uses knowledge compilation to reduce the expensive probabilistic inference to an efficient weighted model counting. Motivated to improve ProbLog's performance we present an approach that optimizes Boolean formulae in order to speed-up knowledge compilation. We identify 7 Boolean subformulae patterns that can be used to re-write Boolean formulae. We implemented an algorithm with polynomial complexity which detects and compacts 6 of these patterns. We employ our method in the inference pipeline of ProbLog and conduct extensive experiments. We show that our compaction method improves knowledge compilation and consecutively the overall inference performance. Furthermore, using compaction reduces the number of time-outs, allowing us to solve previously unsolvable problems.

Using Iterative Deepening for Probabilistic Logic Inference

“…MetaProbLog supports both ROBDDs and sd-DNNFs as a knowledge compilation language. Previous experimental evaluations have shown that ROBDDs are able to solve more problems than sd-DNNFs in the context of MetaProbLog and sd-DNNFs only perform better in conditional queries [12,17]. For that reason, in our experiments we use ROBDDs.…”

“…Furthermore, we would like our iterative inference method to be able to compute the exact inference and detect its computation when that is possible. Further than simply comparing our approach with the usual exact inference, we also used variable compaction for the Alzheimer dataset as presented in [12]. We noticed that variable compaction permitted us to compute more upper bounded queries and that, in general, variable compaction improved the performance (decreased the runtime) of the iterative inference method.…”

“…2. The full integration and compatibility of the new algorithm with all existing optimizations and system features in MetaProbLog, such as: variable compaction [12], general (stratified) negation, multiple queries and evidence. 3.…”