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
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
Anderson, J.A., and Rosenfeld, E. (1988) Neurocomputing. Foundation of Research, MIT Press, Cambridge, MA.
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.
Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion), J. Royal Statist. Soc. B., 36, 192–326.
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.
Cui, W., and Blocley, D.I. (1990) Interval Probability Theory for Evidential Support, Intern. J. of Intelligent Systems, 5, 183–192.
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.
Dean, T., and Kanazawa, K. (1988) Probabilistic temporal reasoning. In: Proc. AAAI 88, 524–528.
Dechter, R., and Pearl, J. (1989) Tree Clustering for Constraint Networks (Research Note), Artificial Intelligence, 38, 353–366.
Dempster, A.P., and Kong, A. (1988) Uncertain evidence and artificial analysis, Research Report S-120, Dept. of Statistics, Harvard University, Cambridge, Massachusetts.
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.
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.
Edwards, D., and Kreiner, S. (1983) The analysis of contingency tables by graphical models, 70, Biometrika 553–565.
Frydenberg, M., and Lauritzen, S.L. (1989) Decomposition of maximum likelihood in mixed graphical interaction models, Biometrika, 76, 539–555.
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.
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.
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).
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.
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.
Halpern, J.Y., and Rabin, M. (1987) A logic to reason about likelihood, Artificial Intelligence, 32, 379–406.
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.
Jaynes, E.T. (1982) On the rationale of maximum entropy methods, Proc. IEEE, 70, 939–952.
Jensen, F.V. (1988) Discussion of [Lauritzen and Spiegelhalter 1988].
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.
Kanal, L.N., and Lemmer, J.F., eds. (1986) Uncertainty in Artificial Intelligence, North-Holland, Amsterdam.
Kim, J. and Pearl, J. (1983) A computational model for causal and diagnostic reasoning in inference systems. Proc. IJCAI 83, Karlsruhe, 190–193.
Kjaerulff, U. (1990) Triangulation of graphs-allgorithms giving small total state space, Technical report R-90–09, Aalborg University, Aalborg.
Laskey, K.B. (1990) Adapting Connectionist Learning to Bayes Networks, Int. J. of Approx. Reasoning, 4, 261–282.
Lauritzen, S.L., Speed, T.P., and Vijayan, K. (1984) Decomposable graphs and hypergraphs, Journal of the Australian Mathematical Society, A, 36, 12–29.
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.
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.
Maier, D. (1983) The theory of Relational databases. Computer Science Press.
Paris, J.B., and Vencovska, A. (1988) On the applicability of maximum entropy to inexact reasoning, Int. J. of Approx. Reasoning, 3, 1–34.
Paris, J.B., and Vencovska, A. (1990) A note on the inevitability of maximum entropy, Int. J. of Approx. Reasoning, 4, 183–223.
Pearl J. (1986) Fusion, propagation and structuring in belief networks, Artificial Intelligence, 29, 241–288.
Pearl, J. (1987a) Evidential reasoning using stochastic simulation of causal models (Research note), Artificial Intelligence, 32, 245–258.
Pearl, J. (1987b) Distributed revision of composite beliefs, Artificial Intelligence, 33, 173–215.
Pearl, J. (1988) Probabilistic reasoning in intelligent systems, Morgan Kaufmann, San Mateo.
Pitarelli, M. (1990) Probabilistic databases for decision analysis, Int. J. of Intell. Systems, 5, 209–236.
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.
Shafer, G., Shenoy, P.P., and Mellouli, K. (1987) Propagating belief functions in qualitative Markov trees, Intern. J. of Approx. Reasoning, 1, 349–400.
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.
Smets, P. (1988) Discussion of [Lauritzen and Spiegelhalter 1988].
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.
Spiegelhalter, D.J., and Lauritzen, S.L. (1990) Sequential updating of conditional probabilities on directed graphical structures, Networks, 20, 579–605.
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.
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.
Wermuth, N. and Lauritzen, S.L. (1983) Graphical and recursive models for contingency tables. Biometrika, 70, 537–552.
Zarley, D., Hsia, Y.T., and Shafer, G. (1988) Evidential reasoning using DELIEF. Proc. AAAI 88, Morgan Kaufmann, 205–209.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Golmard, JL. (1993). Probabilistic Inference in Artificial Intelligence: The Method of Bayesian Networks. In: Dubucs, JP. (eds) Philosophy of Probability. Philosophical Studies Series, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8208-7_11
Download citation
DOI: https://doi.org/10.1007/978-94-015-8208-7_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4301-6
Online ISBN: 978-94-015-8208-7
eBook Packages: Springer Book Archive