A Recursive Model-Reduction Method for Approximate Inference in Gaussian Markov Random Fields

This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise yet faithful model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable represen...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Jason K. Johnson, Alan S. Willsky
• Keywords: Blanket Models, Cavity Models, Near-optimal Inference, TIP 2008