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Variations on undirected graphical models and their relationships. (English) Zbl 1302.60031

Summary: We compare alternative definitions of undirected graphical models for discrete, finite variables. S. L. Lauritzen [Graphical models. Oxford: Oxford Univ. Press (1998; Zbl 0907.62001)] has provided several definitions of such models and described their relationships. He showed that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. D. Heckerman et al. [J. Mach. Learn. Res. 1, No. 1, 49–75 (2001; Zbl 1008.68132)] have described another definition of undirected graphical models for strictly positive distributions. They showed that this definition agrees with those of Lauritzen [loc.cit.]again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [loc.cit.]to arbitrary distributions and show how this definition relates to those of Lauritzen [loc.cit.]in the general case.

MSC:

60E05 Probability distributions: general theory
62H99 Multivariate analysis
68T30 Knowledge representation
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References:

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