Skip to main content

Factorization of Sparse Bayesian Networks

  • Chapter

Part of the book series: Studies in Computational Intelligence ((SCI,volume 199))

Abstract

This paper shows how an efficient and parallel algorithm for inference in Bayesian Networks (BNs) can be built and implemented combining sparse matrix factorization methods with variable elimination algorithms for BNs. This entails a complete separation between a first symbolic phase, and a second numerical phase.

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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Colla, E.C.: Aplicação de Técnicas de Fatoração de Matrizes Esparsas para Inferência em Redes Bayesianas. Ms.S. Thesis, MAC-IME-USP, Institute of Mathematics and Statistics, University of São Paulo (2007)

    Google Scholar 

  • Cozman, F.G.: Generalizing variable elimination in Bayesian networks. IBERAMIA-SBIA, Workshop proceedings. São Paulo, Tec. Art, pp. 27–32 (2000)

    Google Scholar 

  • Mandani, A., Heckerman, D., Wellman, M.P.: Real-world applications of Bayesian networks. Comm. of the ACM 38(3), 24–26 (1995)

    Article  Google Scholar 

  • Dechter, R.: Bucket elimination: An unifying framework for probabilistic inference. In: 12th UAI proceedings, pp. 211–219. Morgan Kaufmann Publishers, San Francisco (1996)

    Google Scholar 

  • George, A., Gilbert, J.R., Liu, J.W.H. (eds.): Graph Theory and Sparse Matrix Computation. Springer, NY (1993)

    MATH  Google Scholar 

  • Jensen, F.V.: An introduction to Bayesian networks. Springer, NY (1996)

    Google Scholar 

  • Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. J. Royal Statistical Soc., B 50(2), 157–224 (1988)

    MATH  MathSciNet  Google Scholar 

  • Pearl, J.: Probabilistic reasoning in intelligent systems: Networks of plausive inference. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  • Pissanetzky, S.: Sparse matrix technology. Academic Press, New York (1984)

    MATH  Google Scholar 

  • Shachter, R.: Bayes-ball: The rational pastime (for determining irrelevance and requisite information in belief networks and influence diagrams). In: 14th UAI proceedings, pp. 480–487. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  • Stern, J.M.: Simulated Annealing with a Temperature Dependent Penalty Function. ORSA Journal on Computing 4, 311–319 (1992)

    MATH  Google Scholar 

  • Stern, J.M.: Esparsidade, Estrutura, Estabilidade e Escalonamento em Álgebra Linear Computacional. IX Escola de Computação. UFPE, Recife (1994)

    Google Scholar 

  • Stern, J.M.: Decoupling, Sparsity, Randomization, and Objective Bayesian Inference. Cybernetics and Human Knowing 15(2), 49–68 (2008a)

    Google Scholar 

  • Stern, J.M.: Cognitive Constructivism and the Epistemic Significance of Sharp Statistical Hypotheses. Tutorial book for MaxEnt, The 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, July 06-11, Boracéia, São Paulo, Brazil (2008b)

    Google Scholar 

  • Stern, J.M., Vavasis, S.A.: Nested Dissection for Sparse Nullspace Bases. SIAM Journal on Matrix Analysis and Applications 14(3), 766–775 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  • Stern, J.M., Vavasis, S.A.: Active Set Algorithms for Problems in Block Angular Form. Computational and Applied Mathemathics 12(3), 199–226 (1994)

    MathSciNet  Google Scholar 

  • van der Vorst, H.A., van Dooren, P. (eds.): Parallel Algorithms for Numerical Linear Algebra. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

  • Zhang, N.L., Poole: Exploiting casual independence in Bayesian network inference. Journal of Artificial Intelligence Research, 301–328 (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Stern, J.M., Colla, E.C. (2009). Factorization of Sparse Bayesian Networks. In: Nakamatsu, K., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds) New Advances in Intelligent Decision Technologies. Studies in Computational Intelligence, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00909-9_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00909-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00908-2

  • Online ISBN: 978-3-642-00909-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics