Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Statistical Models in S
Graphical Models in Applied Multivariate Statistics
Graphical Models in Applied Multivariate Statistics
Properties of markovian subgraphs of a decomposable graph
MICAI'06 Proceedings of the 5th Mexican international conference on Artificial Intelligence
Maximal prime subgraph decomposition of Bayesian networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Suppose that we are interested in modeling for a random vector X and that we are given a set of graphical decomposable models, G1, ..., Gm, for subvectors of X each of which share some variables with at least one of the other models. Under the assumption that the model of X is graphical and decomposable, we propose an approach of searching for models of X based on the given decomposable graphical models. A main idea in this approach is that we combine G1, ..., Gm using graphs of prime separators (section 2). When the true graphical model for the whole data is decomposable, prime separators in a marginal model are also prime separators in a maximal combined model of the marginal models. This property plays a key role in model-combination. The proposed approach is applied to searching for a model of 100 variables for illustration.