|Stochastic Systems Group|
A Multipole-motivated Hierarchical Model for Inference in Large-scale GMRFs
Myung Jin Choi
We propose a multipole-motivated hierarchical model to estimate approximate means and error variances in large-scale Gauss-Markov 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 far-field 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 tree-based 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 long-range correlations.
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