Abstract
We show how Bayesian belief networks (BNs) can be used to model common temporal knowledge. Two approaches to their structuring are proposed. The first leads to BNs with nodes representing states of a process and times spent in such states, and with a graphical structure reflecting the conditional independence assumptions of a Markovian process. A second approach leads to BNs whose topology represents a conditional independence structure between event-times. Once required distributional specifications are stored within the nodes of a BN, this becomes a powerful inference machine capable, for example, of reasoning backwards in time. We discuss computational difficulties associated with propagation algorithms necessary to perform these inferences, and the reasons why we chose to adopt Monte Carlo-based propagation algorithms. Two improvements to existing Monte Carlo algorithms are proposed; an enhancement based on the principle of importance sampling, and a combined technique that exploits both forward and Markov sampling. Finally, we consider Petri nets, a very interesting and general representation of temporal knowledge. A combined approach is proposed, in which the user structures temporal knowledge in Petri net formalism. The obtained Petri net is then automatically translated into an equivalent BN for probability propagation. Inferred conclusions may finally be explained with the aid of Petri nets again.
Similar content being viewed by others
References
D.J. Spiegelhalter, R.C.G. Franklin and K. Bull, Assessment, criticisms and improvement of imprecise subjective probabilities for a medical expert system, in:Proc. 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Canada (1989) p. 335.
T. Dean and K. Kanazawa, Probabilistic temporal reasoning, in:Proc. AAAI-88, St. Paul, Minnesota (Morgan Kaufmann, 1988) p. 254.
S.L. Lauritzen and D.J. Spiegelhalter, Local computations with probabilities on graphical structures and their application to expert systems, J.R. Statist. Soc. B50 (1988) 157.
J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence 29 (1986) 241.
R.D. Shachter, Intelligent probabilistic inference, in:Uncertainty in Artificial Intelligence, eds. L.N. Kanal and J.F. Lemmer (North-Holland, 1986) p. 371.
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Machine Intelligence 6 (1984) 721.
M. Henrion, Propagating uncertainty in Bayesian networks by probabilistic logic sampling, in:Uncertainty in Artificial Intelligence, vol. 2, eds. L.N. Kanal and J.F. Lemmer (North-Holland, 1988) p. 149.
J. Pearl, Evidental reasoning using stochastic simulation of causal models, Artificial Intelligence 32 (1987) 245.
R.M. Chavez, Hypermedia and randomized algorithms for probabilistic expert systems, PhD Thesis, Department of Computer Science, Stanford University, California, USA (1989).
C. Petri, Kommunikation mit Automaten, Ph.D. Dissertation, University of Bonn, Bonn, W. Germany (1962).
J.L. Peterson,Petri Net Theory and the Modeling of Systems (Prentice-Hall, 1981).
S.M. Ross,Stochastic Processes (Wiley, 1983).
D.R. Cox and D. Oakes,Analysis of Survival Data (Chapman and Hall, 1984).
O. Aalen, Nonparametric inference for a family of counting processes, Ann. Statistics 6 (1978) 701.
S.W. Lagakos, C.J. Sommer and M. Zelen, Semi-Markov models for partially censored data, Biometrika 65 (1978) 311.
G.F. Cooper, Probabilistic inference using belief networks is NP-hard, Technical Report KSL-87-27, Medical Computer Science Group, Stanford University, Ca, USA (1987).
D. Clayton, Simulation in hierarchical models, Technical Report, University of Leicester, UK (1988).
A.E. Gelfand and A.F.M. Smith, Sampling based approaches to calculating marginal densities, Technical Report, Department of Mathematics, University of Nottingham, UK (1988).
R. Fung and K.C. Chang, Weighting and integrating evidence for stochastic simulation in Bayesian networks, in:Proc. 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Canada (1989) p. 112.
D.R. Shachter and M.A. Peot, Simulation approaches to general probabilistic inference on belief networks, in:Proc. 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Canada (1989) p. 311.
R.Y. Rubinstein,Simulation and the Monte Carlo Method (Wiley, 1981).
B.D. Ripley,Stochastic Simulation (Wiley, 1987).
S. Quaglini et al., Therapy planning by combining AI and decision theoretic techniques, in:Proc. 2nd AIME Conf., London (Springer, 1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Berzuini, C. Modeling temporal processes via belief networks and Petri nets, with application to expert systems. Ann Math Artif Intell 2, 39–64 (1990). https://doi.org/10.1007/BF01530996
Issue Date:
DOI: https://doi.org/10.1007/BF01530996