High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish struct...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery (ACM)
2013
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| Online Access: | http://hdl.handle.net/1721.1/79410 https://orcid.org/0000-0003-0149-5888 |
| _version_ | 1811094165518286848 |
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| author | Willsky, Alan S. Tan, Vincent Yan Fu Anandkumar, Animashree |
| 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 Willsky, Alan S. Tan, Vincent Yan Fu Anandkumar, Animashree |
| author_sort | Willsky, Alan S. |
| collection | MIT |
| description | We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed algorithm, when the number of samples n=omega(J_{min}^{-2} log p), where p is the number of variables and J_{min} is the minimum (absolute) edge potential of the graphical model. The sufficient conditions for sparsistency are based on the notion of walk-summability of the model and the presence of sparse local vertex separators in the underlying graph. We also derive novel non-asymptotic necessary conditions on the number of samples required for sparsistency. |
| first_indexed | 2024-09-23T15:55:36Z |
| format | Article |
| id | mit-1721.1/79410 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:55:36Z |
| publishDate | 2013 |
| publisher | Association for Computing Machinery (ACM) |
| record_format | dspace |
| spelling | mit-1721.1/794102022-09-29T17:06:15Z High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion Willsky, Alan S. Tan, Vincent Yan Fu Anandkumar, Animashree Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Stochastic Systems Group Willsky, Alan S. Tan, Vincent Yan Fu Anandkumar, Animashree We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed algorithm, when the number of samples n=omega(J_{min}^{-2} log p), where p is the number of variables and J_{min} is the minimum (absolute) edge potential of the graphical model. The sufficient conditions for sparsistency are based on the notion of walk-summability of the model and the presence of sparse local vertex separators in the underlying graph. We also derive novel non-asymptotic necessary conditions on the number of samples required for sparsistency. 2013-07-02T18:40:53Z 2013-07-02T18:40:53Z 2012-01 2011-06 Article http://purl.org/eprint/type/JournalArticle 1532-4435 1533-7928 http://hdl.handle.net/1721.1/79410 Anandkumar, Animashree, Vincent Y. F. Tan, and Alan. S. Willsky. "High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion." Journal of Machine Learning Research 13.1 (2012): 2293-2337. https://orcid.org/0000-0003-0149-5888 en_US http://arxiv.org/abs/1107.1270 Journal of Machine Learning Research 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) MIT Press |
| spellingShingle | Willsky, Alan S. Tan, Vincent Yan Fu Anandkumar, Animashree High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title | High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title_full | High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title_fullStr | High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title_full_unstemmed | High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title_short | High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion |
| title_sort | high dimensional gaussian graphical model selection walk summability and local separation criterion |
| url | http://hdl.handle.net/1721.1/79410 https://orcid.org/0000-0003-0149-5888 |
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