Marginal Markov Subgraph of Bayesian Network and Its Applications
Bayesian networks utilize directed acyclic graphs(DAGs)to constrain con-ditional independencies in multivariate joint probability distribution,so as to realize its modular decomposition in uncertainty reasoning and reduce the computational com-plexity of probabilistic reasoning.They are widely used in probabilistic reasoning,machine learning and causal inference.In practice,if structure learning or statistical inference was performed by adopting the idea of dividing and conquering or model collapsing,we have to establish the marginal models by finding their minimal Markov subgraphs(or minimal independence maps).Therefore,this paper details minimal Markov subgraphs for marginal models of Bayesian networks,and provides the refined characterization on them from the perspectives of statistics and graph theory.For the collapsibility of DAG,this paper gives more intuitive equivalent conditions based on the properties of directed inducing paths,and also proposes some sufficient conditions,which provides more theoretical tools for judging whether the considered models can be collapsible onto local sub-models.
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