Exploiting sparse markov and covariance structure in multiresolution models

• Main Authors: Choi, Myung Jin (Contributor), Chandrasekaran, Venkat (Contributor), Willsky, Alan S. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Laboratory for Information and Decision Systems (Contributor)
• Format: Article
• Language: English
• Published: Association for Computing Machinery / ACM Digital Library, 2011-09-21T17:51:36Z.
• Subjects: Article
• Online Access: Get fulltext

 We consider Gaussian multiresolution (MR) models in which coarser, hidden variables serve to capture statistical dependencies among the finest scale variables. 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 that capture the residual correlations within each scale using sparse covariance structure. Our goal is to learn a tree-structured graphical model connecting variables across different scales, while at the same time learning sparse structure for the conditional covariance 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.