Markovian Combination of Subgraphs of DAGs

S.-H. Kim (Korea)

Keywords

graphical marginalization; dseparateness; dashed line; collision node; smallest ancestral set; separateness condition.

Abstract

Bayesian network models whose model structures are in directed acyclic graphs are useful for representing causal relationships among random variables. Most of the structure learning methods of Bayesian networks are likelihood based employing a greedy search algorithm. In this paper, we propose a structure learning method based on marginal model structures, which is complementary to the likelihood-based method. Suppose that we are interested in modeling for a random vector X whose model structure is given by a DAG and that we are given a set of graphical models, G1, · · · , Gm, for subvectors of X each of which share some variables with at least one of the other models. We propose an approach of searching for model structures of X based on the given graphical models of subvectors. A main idea in this approach is that the node-separateness in a DAG is preserved in its Markovian subgraph and vice versa. We combine G1, · · · , Gm in two steps, union of graphs and check of separateness. These two steps of operation yield model structures which are maximal in the context of set-inclusion of edges. A couple of simulated examples strongly recommend the proposed approach.

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