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A New Uncertainty Measure for Belief Networks with Applications to Optimal Evidential Inferencing
May/June 2001 (vol. 13 no. 3)
pp. 416-425

Abstract—This paper is concerned with the problem of measuring the uncertainty in a broad class of belief networks, as encountered in evidential reasoning applications. In our discussion, we give an explicit account of the networks concerned, and coin them the Dempster-Shafer (D-S) belief networks. We examine the essence and the requirement of such an uncertainty measure based on well-defined discrete event dynamical systems concepts. Furthermore, we extend the notion of entropy for the D-S belief networks in order to obtain an improved optimal dynamical observer. The significance and generality of the proposed dynamical observer of measuring uncertainty for the D-S belief networks lie in that it can serve as a performance estimator as well as a feedback for improving both the efficiency and the quality of the D-S belief network-based evidential inferencing. We demonstrate, with Monte Carlo simulation, the implementation and the effectiveness of the proposed dynamical observer in solving the problem of evidential inferencing with optimal evidence node selection.

[1] K.J. Astrom and B. Wittenmark, Computer-Controlled Systems: Theory and Design. Englewood Cliffs, N.J.: Prentice Hall, 1990.
[2] R.E. Bellman Dynamic Programming. Princeton, N.J.: Princeton Univ. Press, 1957.
[3] P.E. Caines, R. Greiner, and S. Wang, “Classical and Logic-Based Dynamic Observers for Finite Automata,” IMA J. Math. Control&Information, 1991.
[4] C.G. Cassandras, Discrete Event Systems: Modeling and Performance Analysis. Homewood, Ill.: Aksen Assoc. Inc. Publishers and IRWIN, 1993.
[5] E. Charniak, “Bayesian Networks without Tears,” AI Magazine, pp. 50-63, 1991.
[6] T.L. Dean and M.P. Wellman, Planning and Control, San Mateo, Calif.: Morgan Kaufmann, 1991.
[7] A.P. Dempster, “A Generalization of Bayesian Inference,” J. Royal Statistical Soc., vol. 30, pp. 205-247, 1968.
[8] M.C. Desmarais, L. Giroux, S. Larochelle, and S. Leclerc, “Assessing the Structure of Knowledge in a Procedural Domain,” Proc. Cognitive Science Soc., pp. 475-481, 1988.
[9] M.C. Desmarais, “Architecture et Fondements Empiriques d'un Système d'Aide Assistée par Ordinateur pour l'Édition de Texte,” PhD thesis, Universitéde Montéal, Département de Psychologie, 1990.
[10] V.N. Fomin, Discrete Linear Control Systems. Dordrecht, The Netherlands: Kluwer Academic, 1991.
[11] T.D. Garvey, J.D. Lowrance, and M.A. Fischler, “An Inference Technique for Integrating Knowledge from Disparate Sources,” Proc. Int'l Joint Conf. Artifical Intelligence '81, pp. 319-325, 1981.
[12] J. Gordon and E.H. Shortliffe, “The Dempster-Shafer Theory of Evidence,” Rule-Based Expert Systems, B.G. Buchanan and E.H. Shortliffe, eds., Reading, Mass.: Addison-Wesley, 1984.
[13] G.J. Klir, “Generalized Information Theory,” Fuzzy Sets and Systems, vol. 40, pp. 127-142, 1991.
[14] G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic, Theory and Applications, Prentice-Hall, Englewood Cliffs, N.J., 1995.
[15] J. Liu and M.C. Desmarais, “A Method of Learning Implication Networks from Empirical Data: Algorithm and Monte-Carlo Simulation-Based Validation,” IEEE Trans. Knowledge and Data Eng., vol. 9, no. 6, pp. 990-1004, Nov./Dec. 1997.
[16] J. Pearl, Probabilistic Reasoning in Intelligent Systems. San Mateo, Calif.: Morgan Kaufman, 1988.
[17] S.J. Russell and P. Norvig, Artificial Intelligence: A Modern Approach, Prentice Hall, Upper Saddle River, N.J., 1994.
[18] G. Shafer, A Mathematical Theory of Evidence. Princeton, N.J.: Princeton Univ. Press, 1976.
[19] C.E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical J., vol. 27, pp. 379-423, pp. 623-656, 1948.

Index Terms:
Belief networks, uncertainty modeling and management, discrete event dynamical systems, optimal evidential inferencing, controller, observer, entropy, user profile assessment.
Jiming Liu, David A. Maluf, Michel C. Desmarais, "A New Uncertainty Measure for Belief Networks with Applications to Optimal Evidential Inferencing," IEEE Transactions on Knowledge and Data Engineering, vol. 13, no. 3, pp. 416-425, May-June 2001, doi:10.1109/69.929899
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