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 condit...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery / ACM Digital Library
2011
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| Online Access: | http://hdl.handle.net/1721.1/65910 https://orcid.org/0000-0003-0149-5888 |
| _version_ | 1811079995340095488 |
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| author | Choi, Myung Jin Chandrasekaran, Venkat Willsky, Alan S. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Choi, Myung Jin Chandrasekaran, Venkat Willsky, Alan S. |
| author_sort | Choi, Myung Jin |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:23:49Z |
| format | Article |
| id | mit-1721.1/65910 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:23:49Z |
| publishDate | 2011 |
| publisher | Association for Computing Machinery / ACM Digital Library |
| record_format | dspace |
| spelling | mit-1721.1/659102022-09-27T19:15:06Z Exploiting sparse markov and covariance structure in multiresolution models Choi, Myung Jin Chandrasekaran, Venkat Willsky, Alan S. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Willsky, Alan S. Choi, Myung Jin Chandrasekaran, Venkat Willsky, Alan S. 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. United States. Air Force Office of Scientific Research (Grant FA9550-08-1-1080) United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-06-1-0324) Shell International Exploration and Production B.V. Samsung Scholarship Foundation 2011-09-21T17:51:36Z 2011-09-21T17:51:36Z 2009-06 Article http://purl.org/eprint/type/ConferencePaper 9781605585161 1605585165 http://hdl.handle.net/1721.1/65910 Choi, Myung Jin, Venkat Chandrasekaran, and Alan S. Willsky. “Exploiting Sparse Markov and Covariance Structure in Multiresolution Models.” Proceedings of the 26th Annual International Conference on Machine Learning - ICML ’09. Montreal, Quebec, Canada, 2009. 1-8. Copyright 2009 by the author(s)/owner(s). https://orcid.org/0000-0003-0149-5888 en_US http://dx.doi.org/10.1145/1553374.1553397 International Conference on Machine Learning (ICML) 2009 proceedings Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Association for Computing Machinery / ACM Digital Library Choi, MyungJee |
| spellingShingle | Choi, Myung Jin Chandrasekaran, Venkat Willsky, Alan S. Exploiting sparse markov and covariance structure in multiresolution models |
| title | Exploiting sparse markov and covariance structure in multiresolution models |
| title_full | Exploiting sparse markov and covariance structure in multiresolution models |
| title_fullStr | Exploiting sparse markov and covariance structure in multiresolution models |
| title_full_unstemmed | Exploiting sparse markov and covariance structure in multiresolution models |
| title_short | Exploiting sparse markov and covariance structure in multiresolution models |
| title_sort | exploiting sparse markov and covariance structure in multiresolution models |
| url | http://hdl.handle.net/1721.1/65910 https://orcid.org/0000-0003-0149-5888 |
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