Stochastic Systems Group  

Jason Johnson
SSG Master's Student
This talk presents the novel method of recursive cavity modeling as a tractable approach for approximate inference of large GaussMarkov random fields. The main idea is that of recursively dissecting the field, constructing cavity models for each subfield at each level of dissection. The cavity model provides a compact yet faithful model for the surface of one subfield sufficient for inferring other parts of the field. This idea is developed into a twosweep inference/modeling procedure which recursively builds cavity models by an ``upsweep'' procedure and then builds complementary ``blanket models'' by a ``downsweep'' procedure. Marginal models are then produced at the finest level of dissection.
Informationtheoretic principles are employed for model thinning so as to develop compact cavity and blanket models providing tractable inference. Thus, recursive cavity modeling blends recursive inference and iterative modeling methodologies. While the main focus is on Gaussian processes, general principles are emphasized throughout suggesting the applicability of the basic framework to broader classes of Markov random fields. Simulations are performed with randomly generated GaussMarkov random fields on various graphical structures indicating good reliability and scalability of the method.
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