Abstract
A probabilistic expert system provides a graphical representation of a joint probability distribution which enables local computations of probabilities. Dawid (1992) provided a ‘flow- propagation’ algorithm for finding the most probable configuration of the joint distribution in such a system. This paper analyses that algorithm in detail, and shows how it can be combined with a clever partitioning scheme to formulate an efficient method for finding the M most probable configurations. The algorithm is a divide and conquer technique, that iteratively identifies the M most probable configurations.
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References
Andersen, S. K., Olesen, K. G., Jensen, F. V. and Jensen, F. (1990) HUGIN — a shell for building Bayesian belief universes for expert systems. In G. Shafer and J. Pearl (eds) Readings in Uncertainty, pp. 332–337. San Francisco: Morgan Kaufmann.
Cowell, R. G. (1992) BAIES — a probabilistic expert system shell with qualitative and quantitative learning. In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4th edn, pp. 595–600. Oxford: Clarendon Press.
Dawid, A. P. (1992) Applications of a general propagation algorithm for probabilistic expert systems. Statistics and Computing, 2, 25–36.
Jensen, F. V. (1988) Junction trees and decomposable hypergraphs. Judex Research Report, Judex Datasystemer A/S, Aalborg, Denmark F. V. (1990) Calculation in HUGIN of probabilities.
Jensen, F. V., Olesen, K. G. and Andersen, S. K. (1990) An algebra of Bayesian belief universes for knowledge-based systems. Networks, 20, 637–59.
Jensen, F. V. (1996) Introduction to Bayesian Networks. London: UCL Press.
Lauritzen, S. L., Speed, T. P. and Vijayan, K. (1984) Decomposable graphs and hypergraphs. Journal of the Australian Mathematical Society, Series 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). Journal of the Royal Statistical Society Series B, 50, 157–224.
Li, Z. and D'Ambrosio, B. (1993) An efficient approach for finding MAP assignments to belief networks. In Proceedings of the 9th Conference on Uncertainty in AI, pp. 342–9. Washington, Morgan Kaufmann.
Nilsson, D. (1994) An algorithm for finding the M most probable configurations of discrete variables that are specified in probabilistic expert systems. MSc thesis, University of Copenhagen.
Pearl, J. (1986) Fusion, propagation and structuring in belief networks. Artificial Intelligence, 29, 241–88.
Pearl, J. (1988) Probabilistic Reasoning in Intelligence Systems. San Mateo, California: Morgan Kaufmann.
Seroussi, B. and Golmard, J. L. (1994) An algorithm for finding the K most probable configurations in Bayesian networks. International Journal of Approximate Reasoning, 1, 205–33.
Sy, B. K. (1993) A recurrence local computation approach towards ordering composite beliefs in Bayesian belief networks. International Journal of Approximate Reasoning, 8, 17–50.
Xu, H. (1994) Computing marginals from the marginal representation in Markov Trees. Proceedings from the International Conference on Information Processing and Management of Uncertainty in Knowledge-based systems (IPMU), Paris, France, pp. 275–80. Paris, Cite Internationale Universitaire.
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NILSSON, D. An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems. Statistics and Computing 8, 159–173 (1998). https://doi.org/10.1023/A:1008990218483
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DOI: https://doi.org/10.1023/A:1008990218483