Stochastic Systems Group  

A Multipolemotivated Hierarchical Model for Inference in Largescale GMRFs
Myung Jin Choi
SSG, MIT
We propose a multipolemotivated hierarchical model to estimate approximate means and error variances in largescale GaussMarkov random fields (GMRFs) given sparse noisy measurements. The multipole algorithm, originally developed to evaluate the potentials due to distributions of charges, uses interactions between particle clusters to calculate farfield potentials rapidly.
We construct a pyramidal graph by introducing hidden variables at coarser resolutions and allowing local interactions between neighbors at every scale. The inference algorithm on this graph combines treebased algorithms and multigrid methods. This hybrid algorithm requires only a few local iterations at each scale since variables far apart communicate through coarser scales. Preliminary results show that the pyramidal graph provides efficient inference algorithms for models with longrange correlations.
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