Geodesic
Variations on undirected graphical models and their relationships
Kybernetika, Tome 50 (2014) no. 3, pp. 363-377
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We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case.
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case.
DOI : 10.14736/kyb-2014-3-0363
Classification : 60E05, 62H99, 68T30, 68T37
Keywords: graphical model; undirected graph; Markov properties; Gibbs sampler; conditionally specified distributions; dependency network 
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Heckerman, David; Meek, Christopher; Richardson, Thomas. Variations on undirected graphical models and their relationships. Kybernetika, Tome 50 (2014) no. 3, pp. 363-377. doi: 10.14736/kyb-2014-3-0363

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