Marginalization without Summation Exploiting Determinism in Factor Algebra

  • Sander Evers
  • Peter J. F. Lucas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6717)


It is known that solving an exact inference problem on a discrete Bayesian network with many deterministic nodes can be far cheaper than what would be expected based on its treewidth. In this article, we introduce a novel technique for this: to the operations of factor multiplication and factor summation that form the basis of many inference algorithms, we add factor indexing. We integrate this operation into variable elimination, and extend the minweight heuristic accordingly. A preliminary empirical evaluation gives promising results.


Bayesian networks exact inference factor algebra deterministic variables 


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  1. 1.
    Chavira, M., Darwiche, A.: On probabilistic inference by weighted model counting. Artif. Intell. 172(6-7), 772–799 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Corrada Bravo, H., Ramakrishnan, R.: Optimizing MPF queries: decision support and probabilistic inference. In: SIGMOD Conference, pp. 701–712 (2007)Google Scholar
  3. 3.
    Darwiche, A.: Recursive conditioning. Artif. Intell. 126(1-2), 5–41 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dechter, R.: Bucket elimination: A unifying framework for reasoning. Artif. Intell. 113(1-2), 41–85 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Díez, F.J., Galán, S.F.: Efficient computation for the Noisy MAX. Int. J. Intell. Syst. 18(2), 165–177 (2003)CrossRefzbMATHGoogle Scholar
  6. 6.
    Heckerman, D., Breese, J.S.: Causal independence for probability assessment and inference using Bayesian networks. IEEE Transactions on Systems, Man and Cybernetics, Part A 26(6), 826–831 (1996)CrossRefGoogle Scholar
  7. 7.
    Kjærulff, U.: Triangulation of graphs — algorithms giving small total state space. Tech. Rep. R-90-09, Dept. of Mathematics and Computer Science, Aalborg University (1990),
  8. 8.
    Larkin, D., Dechter, R.: Bayesian inference in the presence of determinism. In: Bishop, C.M., Frey, B.J. (eds.) Proceedings of Ninth International Workshop on Artificial Intelligence and Statistics, Key West, USA (2003)Google Scholar
  9. 9.
    Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society. Series B 50(2), 157–224 (1988)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Vomlel, J.: Exploiting functional dependence in Bayesian network inference. In: Darwiche, A., Friedman, N. (eds.) UAI 2002, Proceedings of the 18th Conference in Uncertainty in Artificial Intelligence, University of Alberta, Edmonton, Alberta, Canada, pp. 528–535. Morgan Kaufmann, San Francisco (2002)Google Scholar
  11. 11.
    Zhang, N.L., Poole, D.: Exploiting causal independence in bayesian network inference. J. Artif. Intell. Res. (JAIR) 5, 301–328 (1996)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sander Evers
    • 1
  • Peter J. F. Lucas
    • 1
  1. 1.Institute for Computer and Information SciencesRadboud UniversityNijmegenNetherlands

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