Subgraph Approximations for Large Directed Graphical Models

摘要

Graphical Models provide a powerful tool for the formulation of generalstatistical models. In a previous paper, 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 very large 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. Conditional independence, Gibbs sampler, Kullback-Leibler distance, L1 distance, likelihood weighting, Monte Carlo, Propagation of information.