Marginalization in multidimensional compositional models. (English) Zbl 1249.65010

Summary: Efficient computational algorithms are what made graphical Markov models so popular and successful. Similar algorithms can also be developed for computation with compositional models, which form an alternative to graphical Markov models. In this paper we present a theoretical basis as well as a scheme of an algorithm enabling computation of marginals for multidimensional distributions represented in the form of compositional models.


65C50 Other computational problems in probability (MSC2010)
60E99 Distribution theory
68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: EuDML Link


[1] Badsberg J. H.: An Environment for Graphical Models. Ph.D. Thesis, Aalborg University 1995.
[2] Jensen F. V.: Bayesian Networks and Decision Graphs. Springer Verlag, New York 2001 · Zbl 0973.62005
[3] Jiroušek R.: Marginalization in composed probabilistic models. Proc. 16th Conf. Uncertainty in Artificial Intelligence UAI’00 (C. Boutilier and M. Goldszmidt, Morgan Kaufmann, San Francisco 2000, pp. 301-308
[4] Jiroušek R.: Decomposition of multidimensional distributions represented by perfect sequences. Ann. Math. and Artificial Intelligence 35 (2002), 215-226 · Zbl 1004.60010 · doi:10.1023/A:1014591402750
[5] Jiroušek R.: What is the difference between Bayesian networks and compositional models? In: Proc. 7th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty (H. Noguchi, H. Ishii, M. Inuiguchi, Awaji Yumebutai ICC 2004, pp. 191-196
[6] Lauritzen S. L.: Graphical Models. Clarendon Press, Oxford 1996 · Zbl 1055.62126 · doi:10.1214/ss/1081443232
[7] Shachter R. D.: Evaluating influence diagrams. Oper. Res. 34 (1986), 871-890 · doi:10.1287/opre.34.6.871
[8] Shachter R. D.: Probabilistic inference and influence diagrams. Oper. Res. 36 (1988), 589-604 · Zbl 0651.90043 · doi:10.1287/opre.36.4.589
[9] Shafer G.: Probabilistic Expert Systems. SIAM, Philadelphia 1996 · Zbl 0866.68108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.