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Published 2009 | public
Book Section - Chapter

Exploiting Sparse Markov and Covariance Structure in Multiresolution Models


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.

Additional Information

© 2009 ACM Press. We thank Prof. Hui Chen for discussions about the stock returns example. This research was supported in part by AFOSR through Grant FA9550-08-1-1080, in part under a MURI through AFOSR Grant FA9550-06-1-0324, and in part by Shell International Exploration and Production, Inc. M. J. Choi was partially funded by a Samsung Scholarship.

Additional details

August 20, 2023
January 13, 2024