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Probabilistic Inference by Projected Weighted Model Counting on Horn Clauses

Authors Alexandre Dubray , Pierre Schaus , Siegfried Nijssen

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Author Details

Alexandre Dubray
  • Institute of Information and Communication Technologies, Electonics and Applied Mathematics (ICTEAM), UCLouvain, Belgium
Pierre Schaus
  • Institute of Information and Communication Technologies, Electonics and Applied Mathematics (ICTEAM), UCLouvain, Belgium
Siegfried Nijssen
  • Institute of Information and Communication Technologies, Electonics and Applied Mathematics (ICTEAM), UCLouvain, Belgium

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Alexandre Dubray, Pierre Schaus, and Siegfried Nijssen. Probabilistic Inference by Projected Weighted Model Counting on Horn Clauses. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CP.2023.15

Abstract

Weighted model counting, that is, counting the weighted number of satisfying assignments of a propositional formula, is an important tool in probabilistic reasoning. Recently, the use of projected weighted model counting (PWMC) has been proposed as an approach to formulate and answer probabilistic queries. In this work, we propose a new simplified modeling language based on PWMC in which probabilistic inference tasks are modeled using a conjunction of Horn clauses and a particular weighting scheme for the variables. We show that the major problems of inference for Bayesian Networks, network reachability and probabilistic logic programming can be modeled in this language. Subsequently, we propose a new, relatively simple solver that is specifically optimized to solve the PWMC problem for such formulas. Our experiments show that our new solver is competitive with state-of-the-art solvers on the major problems studied.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic inference problems
  • Computing methodologies → Probabilistic reasoning
  • Mathematics of computing → Bayesian networks
Keywords
  • Model Counting
  • Bayesian Networks
  • Probabilistic Networks

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