Skip to main content

Bayesian Network Inference Using Marginal Trees

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8754))

Abstract

Variable Elimination (VE) answers a query posed to a Bayesian network (BN) by manipulating the conditional probability tables of the BN. Each successive query is answered in the same manner. In this paper, we present an inference algorithm that is aimed at maximizing the reuse of past computation but does not involve precomputation. Compared to VE and a variant of VE incorporating precomputation, our approach fairs favourably in preliminary experimental results.

Supported by NSERC Discovery Grant 238880.

Supported by CNPq - Science Without Borders.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)

    Google Scholar 

  2. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1988)

    Google Scholar 

  3. Zhang, N.L., Poole, D.: A simple approach to Bayesian network computations. In: Proceedings of the Tenth Biennial Canadian Artificial Intelligence Conference, pp. 171–178 (1994)

    Google Scholar 

  4. Cozman, F.G.: Generalizing variable elimination in Bayesian networks. In: Workshop on Probabilistic Reasoning in Artificial Intelligence, Atibaia, Brazil (2000)

    Google Scholar 

  5. Shafer, G.: Probabilistic Expert Systems, vol. 67. Society for Industrial and Applied Mathematics, Philadelphia (1996)

    Book  MATH  Google Scholar 

  6. Tarjan, R., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13(3), 566–579 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Butz, C.J., Yao, H., Hua, S.: A join tree probability propagation architecture for semantic modeling. Journal of Intelligent Information Systems 33(2), 145–178 (2009)

    Article  Google Scholar 

  8. Butz, C.J., Yan, W.: The semantics of intermediate cpts in variable elimination. In: Fifth European Workshop on Probabilistic Graphical Models (2010)

    Google Scholar 

  9. Madsen, A.L., Butz, C.J.: Ordering arc-reversal operations when eliminating variables in Lazy AR propagation. International Journal of Approximate Reasoning 54(8), 1182–1196 (2013)

    Article  Google Scholar 

  10. Madsen, A.L., Jensen, F.V.: Lazy propagation: A junction tree inference algorithm based on Lazy evaluation. Artificial Intelligence 113(1-2), 203–245 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Madsen, A.L.: Improvements to message computation in Lazy propagation. International Journal of Approximate Reasoning 51(5), 499–514 (2010)

    Article  MathSciNet  Google Scholar 

  12. Madsen, A.L., Butz, C.J.: On the importance of elimination heuristics in Lazy propagation. In: Sixth European Workshop on Probabilistic Graphical Models (PGM), pp. 227–234 (2012)

    Google Scholar 

  13. Butz, C.J., Hua, S., Konkel, K., Yao, H.: Join tree propagation with prioritized messages. Networks 55(4), 350–359 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Butz, C., Hua, S.: An improved Lazy-ar approach to Bayesian network inference. In: Nineteenth Canadian Conference on Artificial Intelligence (AI), pp. 183–194 (2006)

    Google Scholar 

  15. Butz, C.J., Konkel, K., Lingras, P.: Join tree propagation utilizing both arc reversal and variable elimination. International Journal of Approximate Reasoning 52(7), 948–959 (2011)

    Article  MathSciNet  Google Scholar 

  16. Butz, C.J., Chen, J., Konkel, K., Lingras, P.: A formal comparison of variable elimination and arc reversal in Bayesian network inference. Intelligent Decision Technologies 3(3), 173–180 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Butz, C.J., de S. Oliveira, J., Madsen, A.L. (2014). Bayesian Network Inference Using Marginal Trees. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11433-0_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11432-3

  • Online ISBN: 978-3-319-11433-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics