Multiscale Gaussian Graphical Models and Algorithms for Large-Scale Inference

Authors:
Myung Jin Choi;Alan S. Willsky
Affiliations:
Massachusetts Institute of Technology, Electrical Engineering and Computer Science, 77 Massachusetts Ave., Cambridge, MA 02139, USA;Massachusetts Institute of Technology, Electrical Engineering and Computer Science, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Venue:
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Year:
2007

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Abstract

We propose a class of multiscale graphical models and algorithms to estimate means and approximate error variances of large-scale Gaussian processes efficiently. Based on emerging techniques for inference on Gaussian graphical models with cycles, we extend traditional multiscale tree models to pyramidal graphs, which incorporate both inter- and intra- scale interactions. In the spirit of multipole algorithms, we develop efficient inference methods in which variables far-apart communicate through coarser resolutions and nearby variables interact at finer resolutions. In addition, we propose methods to update the estimates rapidly when measurements are added or new knowledge of a local region is provided.