Using Four Cost Measures to Determine Arc Reversal Orderings

  • Cory J. Butz
  • Anders L. Madsen
  • Kevin Williams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6717)

Abstract

Four cost measures s1, s2, s3, s4 were recently studied for sorting the operations in Lazy propagation with arc reversal (LPAR), a join tree propagation approach to Bayesian network inference. It has been suggested to use s1 with LPAR, since there is an effectiveness ranking, say s1, s2, s3, s4, when applied in isolation. In this paper, we also suggest to use s1 with LPAR, but to use s2 to break s1 ties, s3 to break s2 ties, and s4 to break s3 ties. Experimental results show that sometimes there is a noticeable gain to be made.

Keywords

Bayesian networks arc reversal join tree propagation 

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References

  1. 1.
    Butz, C.J., Chen, J., Konkel, K., Lingras, P.: A Formal Comparison of Variable Elimination and Arc Reversal in Bayesian Network Inference. Intell. Dec. Analysis 3(3), 173–180 (2009)Google Scholar
  2. 2.
    Butz, C.J., Konkel, K., Lingras, P.: Join Tree Propagation Utilizing both Arc Reversal and Variable Elimination. Intl. J. Approx. Rea. (2010) (in press)Google Scholar
  3. 3.
    Butz, C.J., Hua, S., Konkel, K., Yao, H.: Join Tree Propagation with Prioritized Messages. Networks 55(4), 350–359 (2010)MathSciNetMATHGoogle Scholar
  4. 4.
    Butz, C.J., Yao, H., Hua, S.: A Join Tree Probability Propagation Architecture for Semantic Modelling. J. Int. Info. Sys. 33(2), 145–178 (2009)CrossRefGoogle Scholar
  5. 5.
    Cooper, G.F.: The Computational Complexity of Probabilistic Inference using Bayesian Belief Networks. Art. Intel. 42(2-3), 393–405 (1990)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, New York (2009)CrossRefMATHGoogle Scholar
  7. 7.
    Hansen, P.F., Pedersen, P.T.: Risk Analysis of Conventional and Solo Watch Keeping. Research Report, Department of Naval Architecture and Offshore Engineering. Technical University of Denmark (1998)Google Scholar
  8. 8.
    Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs. Springer, New York (2007)CrossRefMATHGoogle Scholar
  9. 9.
    Kjaerulff, U.B., Madsen, A.L.: Bayesian Networks and Influence Diagrams: a Guide to Construction and Analysis. Springer, New York (2008)CrossRefMATHGoogle Scholar
  10. 10.
    Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. The MIT Press, Cambridge (2009)MATHGoogle Scholar
  11. 11.
    Kristensen, K., Rasmussen, I.A.: The use of a Bayesian Network in the Design of a Decision Support System for Growing Malting Barley without use of Pesticides. Computers and Electronics in Agriculture 33, 192–217 (2002)CrossRefGoogle Scholar
  12. 12.
    Madsen, A.L.: An Empirical Evaluation of Possible Variations of Lazy Propagation. In: 20th Conference in Uncertainty in Artificial Intelligence, pp. 366–373. AUAI Press, Arlington (2004)Google Scholar
  13. 13.
    Madsen, A.L.: Variations over the Message Computation Algorithm of Lazy Propagation. IEEE Trans. Sys. Man Cyb. B 36, 636–648 (2006)CrossRefGoogle Scholar
  14. 14.
    Madsen, A.L.: Improvements to Message Computation in Lazy Propagation. Intl. J. Approx. Rea. 51(5), 499–514 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Madsen, A.L., Jensen, F.V.: A Junction Tree Inference Algorithm based on Lazy Evaluation. Art. Intel. 113(1-2), 203–245 (1999)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Neapolitan, R.E.: Probabilistic Methods for Bioinformatics with an Introduction to Bayesian Networks. Morgan Kaufmann, New York (2009)MATHGoogle Scholar
  17. 17.
    Olmsted, S.: On Representing and Solving Decision Problems. Ph.D. Thesis, Department of Engineering Economic Systems. Stanford University, Stanford, California (1983)Google Scholar
  18. 18.
    Pearl, P.: Probabilistic Reasoning Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)MATHGoogle Scholar
  19. 19.
    Pourret, O., Naim, P., Marcot, B. (eds.): Bayesian Networks: A Practical Guide to Applications. Wiley, New York (2008)MATHGoogle Scholar
  20. 20.
    Shachter, R.: Evaluating Influence Diagrams. Oper. Research 34, 871–882 (1986)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Shafer, G.: Probabilistic Expert Systems. SIAM, Philadelphia (1996)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Cory J. Butz
    • 1
  • Anders L. Madsen
    • 2
  • Kevin Williams
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada
  2. 2.HUGIN EXPERT A/SAalborgDenmark

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