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Exploiting Sparse Markov and Covariance Structure in Multiresolution Models

Choi, Myung Jin and Chandrasekaran, Venkat and Willsky, Alan S. (2009) Exploiting Sparse Markov and Covariance Structure in Multiresolution Models. In: Proceedings of the 26th Annual International Conference on Machine Learning. ACM International Conference Proceeding Series. No.382. ACM Press , New York, pp. 177-184. ISBN 978-1-60558-516-1.

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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.

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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.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-1080
Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI)FA9550-06-1-0324
Shell International Exploration and Production, Inc.UNSPECIFIED
Samsung ScholarshipUNSPECIFIED
Record Number:CaltechAUTHORS:20121008-111307673
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34755
Deposited By: Tony Diaz
Deposited On:08 Oct 2012 19:52
Last Modified:23 Aug 2016 10:19

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