Skip to main content
SpringerLink
Log in

Evidence Propagation in Credal Networks: An Exact Algorithm Based on Separately Specified Sets of Probability

  • Conference paper
  • First Online:
Advances in Artificial Intelligence (SBIA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2507))

Included in the following conference series:

Abstract

Probabilistic models and graph-based independence languages have often been combined in artificial intelligence research. The Bayesian network formalism is probably the best example of this type of association. In this article we focus on graphical structures that associate graphs with sets of probability measures — the result is referred to as a credal network. We describe credal networks and review an algorithm for evidential reasoning that we have recently developed. The algorithm substantially simplifies the computation of upper and lower probabilities by exploiting an independence assumption (strong independence) and a representation based on separately specified sets of probability measures. The algorithm is particularly efficient when applied to polytree structures. We then discuss a strategy for approximate reasoning in multi-connected networks, based on conditioning.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Campos, L. M. de, Moral, S.: Independence concepts for convex sets of probabilities. Proc. of the XI Conf. on Uncertainty in Artificial Intelligence, Montreal, Canada (1995) 108–115.

    Google Scholar 

  2. Cano, J., Delgado, M., Moral, S.: An axiomatic framework for propagating uncertainty in directed acyclic networks. International Journal of Approximate Reasoning, (1993) 8:253–280.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cano, A., Cano, J. E., Moral, S.: Convex sets of probabilities propagation by simulated annealing. IPMU’94, Paris France (1994) 978–983.

    Google Scholar 

  4. Cano, A., Moral, S.: A genetic algorithm to approxiamte convex sets of probabilities. IPMU’96, Vol. 2, (1999) 859–864.

    Google Scholar 

  5. Cano, A., Moral, S.: Using probabilities trees to compute marginals with imprecise probabilities. TR-DECSAI-00-02-14, University of Granada, (2000).

    Google Scholar 

  6. Charniak, E.: Bayesian Networks without tears. AI Magazine, Vol. 12. 4 (1994) 50–63.

    Google Scholar 

  7. Couso, I. Moral, S., Walley, P.: Examples of independence for imprecise probabilities. 1st ISIPTA, Ghent Belgium (1999).

    Google Scholar 

  8. Cozman, F. G.: Credal networks. Artificial Intelligence (2000) 1–35.

    Google Scholar 

  9. Cozman, F. G.: Generalizing variable elimination in Bayesian networks. Workshop on Probabilistic Reasoning in Artificial Intelligence-IBERAMIA/SBIA, Atibaia, Brazil (2000).

    Google Scholar 

  10. Dechter, R.: Bucket elimination: A unifying framework for probabilistic inference. Proc. of the XII Conf. on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA (1996) 211–219.

    Google Scholar 

  11. Edelsbrunner, H.: Algorithms in combinatorial geometry. Springer-Verlag (1987).

    Google Scholar 

  12. Fagiuoli, E., Zaffalon, M.: 2U: an exact interval propagaion algorithm for polytrees with binary variables. AI, Elsevier, 106 (1998) 77–107.

    MATH  MathSciNet  Google Scholar 

  13. Giron, F. J., Rios, S.: Quasi-Bayesian behavior: A more realistic approach to decision making? in: Bernado, J. M., DeGroot, J.H., Lindley, J. H. Smith, A. F. M. (eds.) Bayesian Statistics, University Press, Valencia, (1980) 17–38.

    Google Scholar 

  14. Ha, V. A. et al: Geometric foundations for interval-based probabilities. Annals of Mathematics and Artificial Intelligence, Vol. 24, 1-4 (1998) 1–21.

    Article  MATH  MathSciNet  Google Scholar 

  15. Jensen, F. V., Olensen, K. G., Andersen, S. K.: An algebra of Bayesian belief universes for Knowledge-Based Systems. Networks, Vol. 20. (1990) 637–659.

    Article  MATH  MathSciNet  Google Scholar 

  16. Neapolitan, R.E.: Probabilistic reasoning in expert systems. Theory and algorithms. John Willey and Sons, New York, (1990).

    Google Scholar 

  17. Pearl, J.: Probabilistic reasoning in intelligent systems. Networks of Plausible Inference. Morgan Kaufmann Publishers, San Mateo CA (1988).

    Google Scholar 

  18. Rocha, J.C. F. da, Cozman, F. G.: Inference with Separately Specified Sets of Probabilities in Credal Networks, Proc. of the Conf. on Uncertainty in Artificial Intelligence, Edmonton, Canada, (2002).

    Google Scholar 

  19. Tessem, B.: Interval Probability propagation. Int. Journal of Approximated Reasonin 7, (1995) 95–120.

    Article  MathSciNet  Google Scholar 

  20. Zhang, N.L., Poole, D. Explointing causal independence in Bayesian networks inference. Journal of Artificial Intelligence Research, 5 (1996) 301–328.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Escola Politécnica, Universidade de São Paulo, Av. Prof. Mello Moraes, 2231, 05508-900, São Paulo,SP, Brazil

    José Carlos F. da Rocha & Fabio G. Cozman

  2. Deinfo, Universidade Estadual de Ponta Grossa, 84010.790, Ponta Grossa, PR, Brazil

    José Carlos F. da Rocha

Authors
  1. José Carlos F. da Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio G. Cozman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Automação e Sistemas, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, SC, Brazil

    Guilherme Bittencourt

  2. Centro de Informática, Universidade Federal de Pernambuco, Cx. Postal 7851, 50732-970, Recife, PE, Brazil

    Geber L. Ramalho

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

da Rocha, J.C.F., Cozman, F.G. (2002). Evidence Propagation in Credal Networks: An Exact Algorithm Based on Separately Specified Sets of Probability. In: Bittencourt, G., Ramalho, G.L. (eds) Advances in Artificial Intelligence. SBIA 2002. Lecture Notes in Computer Science(), vol 2507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36127-8_36

Download citation

  • DOI: https://doi.org/10.1007/3-540-36127-8_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00124-9

  • Online ISBN: 978-3-540-36127-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation