Probabilistic Inference in Artificial Intelligence: The Method of Bayesian Networks

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.

[1]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[2]  D. Edwards,et al.  The analysis of contingency tables by graphical models , 1983 .

[3]  Gregory F. Cooper,et al.  Probabilistic inference in multiply connected belief networks using loop cutsets , 1990, Int. J. Approx. Reason..

[4]  Kristian G. Olesen,et al.  HUGIN - A Shell for Building Bayesian Belief Universes for Expert Systems , 1989, IJCAI.

[5]  David Maier,et al.  The Theory of Relational Databases , 1983 .

[6]  W. Cui,et al.  Interval probability theory for evidential support , 1990, Int. J. Intell. Syst..

[7]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[8]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[9]  Michael Pittarelli,et al.  Probabilistic databases for decision analysis , 1990, Int. J. Intell. Syst..

[10]  Glenn Shafer,et al.  Evidential Reasoning Using DELEF , 1988, AAAI.

[11]  Jeff B. Paris,et al.  A note on the inevitability of maximum entropy , 1990, Int. J. Approx. Reason..

[12]  Didier Dubois,et al.  Inference in Possibilistic Hypergraphs , 1990, IPMU.

[13]  L. N. Kanal,et al.  Uncertainty in Artificial Intelligence 5 , 1990 .

[14]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[15]  N. Wermuth,et al.  Graphical and recursive models for contingency tables , 1983 .

[16]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  David J. Spiegelhalter,et al.  Sequential updating of conditional probabilities on directed graphical structures , 1990, Networks.

[18]  T. Speed,et al.  Decomposable graphs and hypergraphs , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[19]  Augustine Kong,et al.  Uncertain evidence and artificial analysis , 1990 .

[20]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[21]  Judea Pearl,et al.  Distributed Revision of Composite Beliefs , 1987, Artif. Intell..

[22]  Judea Pearl,et al.  A Computational Model for Causal and Diagnostic Reasoning in Inference Systems , 1983, IJCAI.

[23]  Khaled Mellouli,et al.  Propagating belief functions in qualitative Markov trees , 1987, Int. J. Approx. Reason..

[24]  Thomas L. Dean,et al.  Probabilistic Temporal Reasoning , 1988, AAAI.

[25]  Benjamin N. Grosof,et al.  An inequality paradigm for probabilistic knowledge the augmented logic of conditional probability intervals , 1985, UAI 1985.

[26]  David J. Spiegelhalter,et al.  Probabilistic Reasoning in Predictive Expert Systems , 1985, UAI.

[27]  T. Speed,et al.  Markov Fields and Log-Linear Interaction Models for Contingency Tables , 1980 .

[28]  Judea Pearl,et al.  Learning Link-Probabilities in Causal Trees , 1986, UAI 1986.

[29]  Jeff B. Paris,et al.  On the applicability of maximum entropy to inexact reasoning , 1989, Int. J. Approx. Reason..

[30]  Judea Pearl,et al.  Evidential Reasoning Using Stochastic Simulation of Causal Models , 1987, Artif. Intell..

[31]  Maria Zemankova,et al.  Intelligent Systems: State of the Art and Future Directions , 1990 .

[32]  Ronald L. Rivest,et al.  A non-iterative maximum entropy algorithm , 1986, UAI.

[33]  Carlo Berzuini Representing Time in Causal Probabilistic Networks , 1989, UAI.

[34]  Kristian G. Olesen,et al.  An algebra of bayesian belief universes for knowledge-based systems , 1990, Networks.

[35]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[36]  M. Frydenberg,et al.  Decomposition of maximum likelihood in mixed graphical interaction models , 1989 .

[37]  Peter C. Cheeseman,et al.  A Method of Computing Generalized Bayesian Probability Values for Expert Systems , 1983, IJCAI.

[38]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[39]  Joseph Y. Halpern,et al.  A Logic to Reason about Likelihood , 1987, Artif. Intell..

[40]  Kathryn B. Laskey Adapting connectionist learning to Bayes networks , 1990, Int. J. Approx. Reason..

[41]  E. Jaynes On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.