Subgraph Approximations for Directed Graphical Models
Graphical Models provide a powerful tool for the formulation of general statistical models. In a previous paper, (Yiannoutsos and Gelfand, 1991), the authors argued that sampling-based techniques provide a unified approach for the analysis of graphical models under general distributional specifications. These techniques include both noniterative and iterative Monte Carlo.
Our concern here is with moderate to large possibly highly connected graphical models whose size and complexity may prohibit analysis within a reasonable time frame. Typically in large systems however, interest focuses on the behavior of only a few critical nodes. Our proposal is to develop, for a particular node, an approximating subgraph which contains virtually as much information about the variable as the full network, but by virtue of its reduced size, enables rapid computational investigation. We provide an illustration using a 40-node graph. Though this is not as large as we would envision in practice, it is convenient in permitting full model calculations to enable assessment of our approximations.
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