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Abstract

Recent algorithms for model counting and compilation work by decomposing a CNF into syntactically independent components through variable splitting, and then solving the components recursively and independently. In this paper, we observe that syntactic component analysis can miss decomposition opportunities because the syntax may hide existing semantic independence, leading to unnecessary variable splitting. Moreover, we show that by applying a limited resolution strategy to the CNF prior to inference, one can transform the CNF to syntactically reveal such semantic independence. We describe a general resolution strategy for this purpose, and a more specific one that utilizes problem–specific structure. We apply our proposed techniques to CNF encodings of Bayesian networks, which can be used to answer probabilistic queries through weighted model counting and/or knowledge compilation. Experimental results demonstrate that our proposed techniques can have a large effect on the efficiency of inference, reducing time and space requirements significantly, and allowing inference to be performed on many CNFs that exhausted resources previously.

Keywords

Bayesian Network Decomposition Algorithm Truth Table Resolution Strategy Variable Splitting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
  2. 2.
  3. 3.
  4. 4.
  5. 5.
    Bacchus, F., Dalmao, S., Pitassi, T.: Dpll with caching: A new algorithm for #SAT and Bayesian inference. Electronic Colloquium on Computational Complexity (ECCC) 10(003) (2003)Google Scholar
  6. 6.
    Bayardo, R., Pehoushek, J.: Counting models using connected components. In: AAAI, pp. 157–162 (2000)Google Scholar
  7. 7.
    Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context–specific independence in Bayesian networks. In: Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 115–123 (1996)Google Scholar
  8. 8.
    Chavira, M., Darwiche, A.: Compiling Bayesian networks with local structure. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1306–1312 (2005)Google Scholar
  9. 9.
    Chavira, M., Darwiche, A., Jaeger, M.: Compiling relational Bayesian networks for exact inference. In: Proceedings of the Second European Workshop on Probabilistic Graphical Models (PGM), pp. 49–56 (2004)Google Scholar
  10. 10.
    Darwiche, A.: On the tractability of counting theory models and its application to belief revision and truth maintenance. Journal of Applied Non-Classical Logics 11(1-2), 11–34 (2001)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Darwiche, A.: A compiler for deterministic, decomposable negation normal form. In: Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI), pp. 627–634. AAAI Press, Menlo Park (2002)Google Scholar
  12. 12.
    Darwiche, A.: A logical approach to factoring belief networks. In: Proceedings of KR, pp. 409–420 (2002)Google Scholar
  13. 13.
    Darwiche, A.: New advances in compiling CNF to decomposable negational normal form. In: Proceedings of European Conference on Artificial Intelligence, pp. 328–332 (2004)Google Scholar
  14. 14.
    Hayes, J.P.: Introduction to Digital Logic Design. Addison-Wesley, Reading (1993)Google Scholar
  15. 15.
    Huang, J., Darwiche, A.: Dpll with a trace: From sat to knowledge compilation. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 156–162 (2005)Google Scholar
  16. 16.
    Mirsalehi, M.M., Gaylord, T.K.: Logical minimization of multilevel coded functions. Applied Optics 25, 3078–3088 (1986)CrossRefGoogle Scholar
  17. 17.
    Sang, T., Bacchus, F., Beame, P., Kautz, H.A., Pitassi, T.: Combining component caching and clause learning for effective model counting. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, Springer, Heidelberg (2005)Google Scholar
  18. 18.
    Sang, T., Beame, P., Kautz, H.: Solving Bayesian networks by weighted model counting. In: Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI 2005), vol. 1, pp. 475–482. AAAI Press, Menlo Park (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mark Chavira
    • 1
  • Adnan Darwiche
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaLos Angeles

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