Skip to main content

Importance Sampling in Bayesian Networks Using Antithetic Variables

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2143))

Abstract

In this paper we introduce an improvement over importance sampling propagation algorithms in Bayesian networks. The difference with respect to importance sampling is that during the simulation, configurations are obtained using antithetic variables (variables with negative correlation), achieving a reduction of the variance of the estimation. The performance of the new algorithm is tested by means of some experiments carried out over four large real-world networks.

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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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. R.R. Bouckaert, E. Castillo, and J.M. Gutiérrez. A modified simulation scheme for inference in Bayesian networks. International Journal of Approximate Reasoning, 14:55–80, 1996.

    Article  MATH  Google Scholar 

  2. G.F. Cooper. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence, 42:393–405, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Dagum and M. Luby. Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artificial Intelligence, 60:141–153, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Dagum and M. Luby. An optimal approximation algorithm for Bayesian inference. Artificial Intelligence, 93:1–27, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  5. K.W. Fertig and N.R. Mann. An accurate approximation to the sampling distribution of the studentized extreme-valued statistic. Technometrics, 22:83–90, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Fung and K.C. Chang. Weighting and integrating evidence for stochastic simulation in Bayesian networks. In M. Henrion, R.D. Shachter, L.N. Kanal, and J.F. Lemmer, editors, Uncertainty in Artificial Intelligence, volume 5, pages 209–220. North-Holland (Amsterdam), 1990.

    Google Scholar 

  7. J. Geweke. Antithetic acceleration of Monte Carlo integration in Bayesian inference. Journal of Econometrics, 38:73–89, 1988.

    Article  MATH  Google Scholar 

  8. L.D. Hernández, S. Moral, and A. Salmerón. Importance sampling algorithms for belief networks based on approximate computation. In Proceedings of the Sixth International Conference IPMU’96, volume II, pages 859–864, Granada (Spain), 1996.

    Google Scholar 

  9. L.D. Hernández, S. Moral, and A. Salmerón. A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques. International Journal of Approximate Reasoning, 18:53–91, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  10. C.S. Jensen, A. Kong, and U. Kjærulff. Blocking Gibbs sampling in very large probabilistic expert systems. International Journal of Human-Computer Studies, 42:647–666, 1995.

    Article  Google Scholar 

  11. S.L. Lauritzen and D.J. Spiegelhalter. Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, Series B, 50:157–224, 1988.

    MATH  MathSciNet  Google Scholar 

  12. J. Pearl. Evidential reasoning using stochastic simulation of causal models. Artificial Intelligence, 32:247–257, 1987.

    Article  MathSciNet  Google Scholar 

  13. J. Pearl. Probabilistic reasoning in intelligent systems. Morgan-Kauffman (San Mateo), 1988.

    Google Scholar 

  14. R.Y. Rubinstein. Simulation and the Monte Carlo Method. Wiley (New York), 1981.

    MATH  Google Scholar 

  15. R.Y. Rubinstein and B. Melamed. Modern simulation and modeling. Wiley (New York), 1998.

    MATH  Google Scholar 

  16. A. Salmerón, A. Cano, and S. Moral. Importance sampling in Bayesian networks using probability trees. Computational Statistics and Data Analysis, 34:387–413, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  17. R.D. Shachter and M.A. Peot. Simulation approaches to general probabilistic inference on belief networks. In M. Henrion, R.D. Shachter, L.N. Kanal, and J.F. Lemmer, editors, Uncertainty in Artificial Intelligence, volume 5, pages 221–231. North Holland (Amsterdam), 1990.

    Google Scholar 

  18. N.L. Zhang and D. Poole. Exploiting causal independence in Bayesian network inference. Journal of Artificial Intelligence Research, 5:301–328, 1996.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Salmerón, A., Moral, S. (2001). Importance Sampling in Bayesian Networks Using Antithetic Variables. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-44652-4_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42464-2

  • Online ISBN: 978-3-540-44652-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics