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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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References

  1. Rehan Abdul Aziz, Geoffrey Chu, Christian Muise, and Peter Stuckey. #∃ SAT: Projected model counting. In International Conference on Theory and Applications of Satisfiability Testing 2015. Springer, 2015. Google Scholar
  2. Anicet Bart, Frédéric Koriche, Jean-Marie Lagniez, and Pierre Marquis. An improved CNF encoding scheme for probabilistic inference. In Proceedings of the Twenty-second European Conference on Artificial Intelligence, 2016. Google Scholar
  3. Supratik Chakraborty, Kuldeep S. Meel, and Moshe Y. Vardi. Algorithmic improvements in approximate counting for probabilistic inference: From linear to logarithmic sat calls. In IJCAI, 2016. Google Scholar
  4. Mark Chavira and Adnan Darwiche. Compiling Bayesian networks with local structure. In IJCAI, volume 5, 2005. Google Scholar
  5. Mark Chavira and Adnan Darwiche. Encoding CNFs to empower component analysis. In Theory and Applications of Satisfiability Testing-SAT 2006: 9th International Conference, Seattle, WA, USA, August 12-15, 2006. Proceedings 9. Springer, 2006. Google Scholar
  6. Mark Chavira and Adnan Darwiche. On probabilistic inference by weighted model counting. Artificial Intelligence, 172(6-7), 2008. Google Scholar
  7. Adnan Darwiche. A logical approach to factoring belief networks. KR, 2, 2002. Google Scholar
  8. Luc De Raedt, Angelika Kimmig, and Hannu Toivonen. Problog: A probabilistic prolog and its application in link discovery. In IJCAI, volume 7. Hyderabad, 2007. Google Scholar
  9. Paulius Dilkas and Vaishak Belle. Weighted model counting with conditional weights for Bayesian networks. In Uncertainty in Artificial Intelligence. PMLR, 2021. Google Scholar
  10. William F. Dowling and Jean H. Gallier. Linear-time algorithms for testing the satisfiability of propositional Horn formulae. The Journal of Logic Programming, 1(3), 1984. Google Scholar
  11. Jeffrey M. Dudek, Vu H. N. Phan, and Moshe Y. Vardi. ProCount: Weighted Projected Model Counting with Graded Project-Join Trees. In Chu-Min Li and Felip Manyà, editors, Theory and Applications of Satisfiability Testing endash SAT 2021, Lecture Notes in Computer Science, Cham, 2021. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-80223-3_11.
  12. Leonardo Duenas-Osorio, Kuldeep Meel, Roger Paredes, and Moshe Vardi. Counting-based reliability estimation for power-transmission grids. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 31, 2017. Google Scholar
  13. Daan Fierens, Guy Van den Broeck, Joris Renkens, Dimitar Shterionov, Bernd Gutmann, Ingo Thon, Gerda Janssens, and Luc De Raedt. Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theory and Practice of Logic Programming, 15(3), 2015. Google Scholar
  14. Katherine A. Klise, Michael Bynum, Dylan Moriarty, and Regan Murray. A software framework for assessing the resilience of drinking water systems to disasters with an example earthquake case study. Environmental modelling & software, 95, 2017. Google Scholar
  15. Tuukka Korhonen and Matti Järvisalo. Integrating tree decompositions into decision heuristics of propositional model counters. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2021. Google Scholar
  16. Jean-Marie Lagniez and Pierre Marquis. An Improved Decision-DNNF Compiler. In IJCAI, volume 17, 2017. Google Scholar
  17. Jean-Marie Lagniez and Pierre Marquis. A recursive algorithm for projected model counting. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, 2019. Google Scholar
  18. Wided Medjroubi, Ulf Philipp Müller, Malte Scharf, Carsten Matke, and David Kleinhans. Open data in power grid modelling: New approaches towards transparent grid models. Energy Reports, 3, 2017. Google Scholar
  19. Tian Sang, Paul Beame, and Henry Kautz. Heuristics for fast exact model counting. In Theory and Applications of Satisfiability Testing: 8th International Conference, SAT 2005, St Andrews, UK, June 19-23, 2005. Proceedings 8. Springer, 2005. Google Scholar
  20. Tian Sang, Paul Beame, and Henry Kautz. Solving Bayesian networks by weighted model counting. In Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI-05), volume 1. AAAI Press, 2005. Google Scholar
  21. Marco Scutari. Learning Bayesian networks with the bnlearn R package. arXiv preprint arXiv:0908.3817, 2009. URL: https://arxiv.org/abs/0908.3817.
  22. Shubham Sharma, Subhajit Roy, Mate Soos, and Kuldeep S. Meel. GANAK: A Scalable Probabilistic Exact Model Counter. In IJCAI, volume 19, 2019. Google Scholar
  23. Mate Soos, Stephan Gocht, and Kuldeep S. Meel. Tinted, detached, and lazy cnf-xor solving and its applications to counting and sampling. In International Conference on Computer Aided Verification, 2020. Google Scholar
  24. Mate Soos and Kuldeep S. Meel. Bird: engineering an efficient cnf-xor sat solver and its applications to approximate model counting. In AAAI, 2019. Google Scholar
  25. Ryosuke Suzuki, Kenji Hashimoto, and Masahiko Sakai. Improvement of projected model-counting solver with component decomposition using SAT solving in components. Technical report, JSAI Technical Report, SIG-FPAI-506-07, 2017. Google Scholar
  26. Marc Thurley. sharpSAT-counting models with advanced component caching and implicit BCP. SAT, 4121, 2006. Google Scholar
  27. Jonas Vlasselaer, Angelika Kimmig, Anton Dries, Wannes Meert, and Luc De Raedt. Knowledge compilation and weighted model counting for inference in probabilistic logic programs. In Proceedings of the First Workshop on Beyond NP. AAAI Press, 2016. Google Scholar
  28. Bart Wiegmans. Gridkit: European And North-American Extracts, March 2016. URL: https://doi.org/10.5281/ZENODO.47317.
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