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Anytime Weighted Model Counting with Approximation Guarantees for Probabilistic Inference

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. Anytime Weighted Model Counting with Approximation Guarantees for Probabilistic Inference. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CP.2024.10

Abstract

Weighted model counting (WMC) plays a central role in probabilistic reasoning. Given that this problem is #P-hard, harder instances can generally only be addressed using approximate techniques based on sampling, which provide statistical convergence guarantees: the longer a sampling process runs, the more accurate the WMC is likely to be. In this work, we propose a deterministic search-based approach that can also be stopped at any time and provides hard lower- and upper-bound guarantees on the true WMC. This approach uses a value heuristic that guides exploration first towards models with a high weight and leverages Limited Discrepancy Search to make the bounds converge faster. The validity, scalability, and convergence of our approach are tested and compared with state-of-the-art baseline methods on the problem of computing marginal probabilities in Bayesian networks and reliability estimation in probabilistic graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic inference problems
  • Theory of computation → Probabilistic computation
  • Mathematics of computing → Approximation
Keywords
  • Projected Weighted Model Counting
  • Limited Discrepancy Search
  • Approximate Method
  • Probabilistic Inference

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