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Probabilistic Inference in Artificial Intelligence: The Method of Bayesian Networks

  • Jean-Louis Golmard
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Part of the Philosophical Studies Series book series (PSSP, volume 56)

Abstract

Bayesian networks are formalisms which associate a graphical representation of causal relationships and an associated probabilistic model. They allow to specify easily a consistent probabilistic model from a set of local conditional probabilities. In order to infer the probabilities of some facts, given observations, inference algorithms have to be used, since the size of the probabilistic models is usually large. Several such inference methods are described and illustrated. Less advanced related problems, namely learning, validation, continuous variables, and time, are briefly discussed. Finally, the relationships between the field of Bayesian networks and other scientific domains are reviewed.

Keywords

Conditional Probability Probabilistic Model Bayesian Network Maximal Clique Marginal Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Andersen, S.K., Olesen, K.G., Jensen, F.V., and Jensen, F. (1989) HUGIN-a shell for building Bayesian belief universes for expert systems, Proc. IJCAI 89, Detroit, MI, Morgan-Kaufmann.Google Scholar
  2. Anderson, J.A., and Rosenfeld, E. (1988) Neurocomputing. Foundation of Research, MIT Press, Cambridge, MA.Google Scholar
  3. Berzuini, C. (1990) Representing time in causal probabilistic networks. In: Uncertainty in Artificial Intelligence 5, (M. Henrion, R.D. Shachter, L.N. Kanal, and J.F. Lemmer eds.), North-Holland, Amsterdam, p. 15–28.Google Scholar
  4. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion), J. Royal Statist. Soc. B., 36, 192–326.Google Scholar
  5. Cheeseman, P.C. (1983) A method for computing generalized Bayesian probability values for expert systems. Proc. Eighth International Conference on Artificial Intelligence, Karlsruhe, 198–202.Google Scholar
  6. Cui, W., and Blocley, D.I. (1990) Interval Probability Theory for Evidential Support, Intern. J. of Intelligent Systems, 5, 183–192.CrossRefGoogle Scholar
  7. Darroch, J.N., Lauritzen, S.L., and Speed, T.P. (1980) Markov fields and log-linear interaction models for contingency tables. The Annals of Statistics, 8, p. 522–539.CrossRefGoogle Scholar
  8. Dean, T., and Kanazawa, K. (1988) Probabilistic temporal reasoning. In: Proc. AAAI 88, 524–528.Google Scholar
  9. Dechter, R., and Pearl, J. (1989) Tree Clustering for Constraint Networks (Research Note), Artificial Intelligence, 38, 353–366.CrossRefGoogle Scholar
  10. Dempster, A.P., and Kong, A. (1988) Uncertain evidence and artificial analysis, Research Report S-120, Dept. of Statistics, Harvard University, Cambridge, Massachusetts.Google Scholar
  11. Dubois, D., and Prade, H. (1990) Inference in Possibilistic Hypergraphs. Proc. Third International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, 228–230.Google Scholar
  12. Dubois, D., Prade, H., et Toucas, J.M. (1991) Inference with emprecise numerical quantifiers, to appear in: “Intelligent systems: state of the art and future directions,” (Z. Ras et M. Zemanka eds.), Ellis Horwood Ltd.Google Scholar
  13. Edwards, D., and Kreiner, S. (1983) The analysis of contingency tables by graphical models, 70, Biometrika 553–565.Google Scholar
  14. Frydenberg, M., and Lauritzen, S.L. (1989) Decomposition of maximum likelihood in mixed graphical interaction models, Biometrika, 76, 539–555.CrossRefGoogle Scholar
  15. Geman, S., and Geman, D. (1984) Stochastic relaxations, Gibbs distributions and the Bayesian restauration of images, IEEE Transaction on Pattern Analysis and Machine Intelligence, 6, 721–742.CrossRefGoogle Scholar
  16. Goldman, S.A., and Rivest, R.L. (1988) A non-iterative maximum entropy algorithm. In: Uncertainty in Artificial Intelligence 2, (J.D. Lemmer and L.N. Kanal eds.), Elsevier Science Publishers, North-Holland, 133–148.Google Scholar
  17. Golmard, J.L. (1988) An approach to uncertain reasoning based on a probabilistic model. Proc. “Expert systems and their applications, ” Avignon, France, p. 97–116, EC2, (in French).Google Scholar
  18. Golmard, J.L., and Mallet, A. (1989) Learning probabilities in causal trees form incomplete databases. Proc. LTCAI-89 Workshop on Knowledge Discovery in Databases, (G. Piatetsky-Shapiro and W. Frawley eds.), Detroit, MI, p. 117–126. Revised version in: (1991) Revue d’Intelligence Artificielle, 5, 93–106.Google Scholar
  19. Groshof, B.N. (1986) An inequality paradigm for probabilistic knowledge-The logic of conditional probability intervals. In: Uncertainty in Artificial Intelligence, (L.N. Kanal and J.F. Lemmer eds.), North-Holland, Amsterdam, p. 259–275.Google Scholar
  20. Halpern, J.Y., and Rabin, M. (1987) A logic to reason about likelihood, Artificial Intelligence, 32, 379–406.CrossRefGoogle Scholar
  21. Henrion, M. (1988) Propagating uncertainty in Bayesian networks by probabilistic logic sampling. In: Uncertainty in Artificial Intelligence 2, (J.F. Lemmer and L.N. Kanal eds.), Elsevier Science Publishers, North-Holland, 149–163.Google Scholar
  22. Jaynes, E.T. (1982) On the rationale of maximum entropy methods, Proc. IEEE, 70, 939–952.CrossRefGoogle Scholar
  23. Jensen, F.V. (1988) Discussion of [Lauritzen and Spiegelhalter 1988].Google Scholar
  24. Jensen, F.V., Olesen, K.G., and Andersen, S.K. (1990) An algebra of Bayesian belief universes for knowledge based systems. Networks, 20, 637–659.CrossRefGoogle Scholar
  25. Kanal, L.N., and Lemmer, J.F., eds. (1986) Uncertainty in Artificial Intelligence, North-Holland, Amsterdam.Google Scholar
  26. Kim, J. and Pearl, J. (1983) A computational model for causal and diagnostic reasoning in inference systems. Proc. IJCAI 83, Karlsruhe, 190–193.Google Scholar
  27. Kjaerulff, U. (1990) Triangulation of graphs-allgorithms giving small total state space, Technical report R-90–09, Aalborg University, Aalborg.Google Scholar
  28. Laskey, K.B. (1990) Adapting Connectionist Learning to Bayes Networks, Int. J. of Approx. Reasoning, 4, 261–282.CrossRefGoogle Scholar
  29. Lauritzen, S.L., Speed, T.P., and Vijayan, K. (1984) Decomposable graphs and hypergraphs, Journal of the Australian Mathematical Society, A, 36, 12–29.CrossRefGoogle Scholar
  30. Lauritzen, S.L., and Spiegelhalter, D.J. (1988) Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J. Royal Statist. Soc. B, 50, 157–224.Google Scholar
  31. Levey, H., Low, D.W. (1983) A new algorithm for finding small cycle cutsets, Rept. G 320–2721, IBM Los Angeles Scientific Center, Los Angeles, CA.Google Scholar
  32. Maier, D. (1983) The theory of Relational databases. Computer Science Press.Google Scholar
  33. Paris, J.B., and Vencovska, A. (1988) On the applicability of maximum entropy to inexact reasoning, Int. J. of Approx. Reasoning, 3, 1–34.CrossRefGoogle Scholar
  34. Paris, J.B., and Vencovska, A. (1990) A note on the inevitability of maximum entropy, Int. J. of Approx. Reasoning, 4, 183–223.CrossRefGoogle Scholar
  35. Pearl J. (1986) Fusion, propagation and structuring in belief networks, Artificial Intelligence, 29, 241–288.CrossRefGoogle Scholar
  36. Pearl, J. (1987a) Evidential reasoning using stochastic simulation of causal models (Research note), Artificial Intelligence, 32, 245–258.CrossRefGoogle Scholar
  37. Pearl, J. (1987b) Distributed revision of composite beliefs, Artificial Intelligence, 33, 173–215.CrossRefGoogle Scholar
  38. Pearl, J. (1988) Probabilistic reasoning in intelligent systems, Morgan Kaufmann, San Mateo.Google Scholar
  39. Pitarelli, M. (1990) Probabilistic databases for decision analysis, Int. J. of Intell. Systems, 5, 209–236.CrossRefGoogle Scholar
  40. Roizen, I., and Pearl, J. (1986) Learning Link-Probabilities in Causal Trees. Proc. Second Workshop on Uncertainty in Artificial Intelligence, Philadelphia, PA, p. 211–214.Google Scholar
  41. Shafer, G., Shenoy, P.P., and Mellouli, K. (1987) Propagating belief functions in qualitative Markov trees, Intern. J. of Approx. Reasoning, 1, 349–400.CrossRefGoogle Scholar
  42. Shenoy, P.O., and Shafer, G. (1990) Axioms for probability and belief-function propagation. In: Uncertainty in Artificial Intelligence 4, (R.D. Shachter, T.S. Levitt, L.N. Kanal, and J.F. Lemmer eds.), North-Holland, Amsterdam.Google Scholar
  43. Smets, P. (1988) Discussion of [Lauritzen and Spiegelhalter 1988].Google Scholar
  44. Spiegelhalter, D.J. (1986) Probabilistic reasoning in predictive expert systems. In: Uncertainty in Artificial Intelligence, (L.N. Kanal and J.F. Lemmer eds.), Elsevier Science Publisher, North-Holland, 47–67.Google Scholar
  45. Spiegelhalter, D.J., and Lauritzen, S.L. (1990) Sequential updating of conditional probabilities on directed graphical structures, Networks, 20, 579–605.CrossRefGoogle Scholar
  46. Suermondt, H.J., and Cooper, G.F. (1990) Probabilistic Inference in Multiply Connected Belief Networks using Loop Cutsets, Int. J. of Approx. Reasoning, 4, 283–306.CrossRefGoogle Scholar
  47. Tarjan, R.E. and Yannakakis, M. (1984) Simple linear-time algorithms to test chordiality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclics hypergraphs, SIAM J. Comput., 13, 566–579.CrossRefGoogle Scholar
  48. Wermuth, N. and Lauritzen, S.L. (1983) Graphical and recursive models for contingency tables. Biometrika, 70, 537–552.CrossRefGoogle Scholar
  49. Zarley, D., Hsia, Y.T., and Shafer, G. (1988) Evidential reasoning using DELIEF. Proc. AAAI 88, Morgan Kaufmann, 205–209.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Jean-Louis Golmard
    • 1
  1. 1.Département de BiomathématiquesParisFrance

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