Abstract
This paper is one of many attempts to introduce graphicalMarkov models within Dempster-Shafer theory of evidence. Here we take full advantage of the notion of factorization, which in probability theory (almost) coincides with the notion of conditional independence. In Dempster-Shafer theory this notion can be quite easily introduced with the help of the operator of composition.
Nevertheless, the main goal of this paper goes even further. We show that if a belief network (a D-S counterpart of a Bayesian network) is to be used to support decision, one can apply all the ideas of Lauritzen and Spiegelhalter’s local computations.
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References
Cano, A., Moral, S.: Heuristic algorithms for the triangulation of graphs. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) IPMU 1994. LNCS, vol. 945, Springer, Heidelberg (1995)
Dempster, A.: Upper and lower probabilities induced by a multi-valued mapping. Ann. of Math. Stat. 38, 325–339 (1967)
Dempster, A.P., Kong, A.: Uncertain evidence and artificial analysis. J. Stat. Planning and Inference 20, 355–368 (1988); These are very powerful models for representing and manipulating belief functions in multidimensional spaces
Jensen, F.V.: Bayesian Networks and Decision Graphs. IEEE Computer Society Press, New York (2001)
Jiroušek, R.: Composition of probability measures on finite spaces. In: Geiger, D., Shenoy, P.P. (eds.) Proc. of the 13th Conf. Uncertainty in Artificial Intelligence UAI 1997. Morgan Kaufmann Publ., San Francisco (1997)
Jiroušek, R.: A note on local computations in Dempster-Shafer theory of evidence. Accepted to 7th Symposium on Imprecise Probabilities and Their Applications, Innsbruck (2011)
Jiroušek, R., Vejnarová, J.: Compositional models and conditional independence in evidence theory. Int. J. Approx. Reason. 52, 316–334 (2011)
Jiroušek, R., Vejnarová, J., Daniel, M.: Compositional models of belief functions. In: de Cooman, G., Vejnarová, J., Zaffalon, M. (eds.) Proc. of the 5th Symposium on Imprecise Probabilities and Their Applications, Praha (2007)
Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computation with probabilities on graphical structures and their application to expert systems. J. of Royal Stat. Soc. series B 50, 157–224 (1988)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Shenoy, P.P., Shafer, G.: Axioms for Probability and Belief-Function Propagation. In: Shachter, R.D., Levitt, T., Lemmer, J.F., Kanal, L.N. (eds.) Uncertainty in Artificial Intelligence, vol. 4, North-Holland, Amsterdam (1990)
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Jiroušek, R. (2011). Belief Networks and Local Computations. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_21
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DOI: https://doi.org/10.1007/978-3-642-22833-9_21
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