|Stochastic Systems Group|
Jason K. Johnson
This talk describes recursive cavity modeling as a tractable approach for approximate inference of large Gauss-Markov random fields. The main idea is to recursively disect the field constructing "cavity models" of subfields at each level of dissection. The cavity model is intended as a compact yet faithful model for the surface of one subfield sufficient for inference in adjacent subfields. This idea is developed into a two-sweep inference/modeling procedure which recursively builds cavity models by an "upward pass" and then builds complimentary "blanket models" by a "downward pass."
Model thinning is performed to develop "thin" cavity and blanket models thereby providing tractable inference. This is accomplished by a combination of model selection and information projection (minimizing the Kullback-Leibler divergence). The Akaike information criterion is adapted to this context for model selection. A novel variation of the iterative scaling approach is employed to implement the information projection step.
Thus, the recursive cavity modeling approach blends recursive inference and iterative modeling methodologies. Several examples are presented where we estimate the marginal distributions of partially observed GMRFs defined on a 64 x 64 nearest-neighbor grid (while restricting the complexity of the method so as to insure scalability). The reliability of the method is examined by comparing these estimates to the actual marginals. Such experiments indicate good scalability and reliability of the method.
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