Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure
Author(s)Choi, Myung Jin; Chandrasekaran, Venkat; Willsky, Alan S.
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In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture long-distance dependencies. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales. Our goal is to learn a tree-structured graphical model connecting variables across scales (which translates into sparsity in inverse covariance), while at the same time learning sparse structure for the conditional covariance (not its inverse) within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics. We demonstrate the modeling and inference advantages of our approach over methods that use MR tree models and single-scale approximation methods that do not use hidden variables.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Signal Processing
Institute of Electrical and Electronics Engineers
Myung Jin Choi, V. Chandrasekaran, and A.S. Willsky. “Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure.” Signal Processing, IEEE Transactions on 58.3 (2010): 1012-1024. © Copyright 2010 IEEE
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INSPEC Accession Number: 11105857
multiresolution (MR) models, multipole methods, hidden variables, graphical models, Gauss–Markov random fields