TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models
We propose a new procedure for optimally estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: It requires very little effort to choose the tuning parameter in finite sample settings. Computationally, our procedur...
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| Format: | Article |
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Institute of Mathematical Statistics
2018
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| Online Access: | http://hdl.handle.net/1721.1/114214 https://orcid.org/0000-0003-3582-8898 |
| _version_ | 1826200263962132480 |
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| author | Liu, Han Wang, Lie |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Liu, Han Wang, Lie |
| author_sort | Liu, Han |
| collection | MIT |
| description | We propose a new procedure for optimally estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: It requires very little effort to choose the tuning parameter in finite sample settings. Computationally, our procedure is significantly faster than existing methods due to its tuning-insensitive property. Theoretically, the obtained estimator simultaneously achieves minimax lower bounds for precision matrix estimation under different norms. Empirically, we illustrate the advantages of the proposed method using simulated and real examples. The R package camel implementing the proposed methods is also available on the Comprehensive R Archive Network. |
| first_indexed | 2024-09-23T11:33:48Z |
| format | Article |
| id | mit-1721.1/114214 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:33:48Z |
| publishDate | 2018 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1142142022-10-01T04:28:42Z TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models Liu, Han Wang, Lie Massachusetts Institute of Technology. Department of Mathematics Wang, Lie We propose a new procedure for optimally estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: It requires very little effort to choose the tuning parameter in finite sample settings. Computationally, our procedure is significantly faster than existing methods due to its tuning-insensitive property. Theoretically, the obtained estimator simultaneously achieves minimax lower bounds for precision matrix estimation under different norms. Empirically, we illustrate the advantages of the proposed method using simulated and real examples. The R package camel implementing the proposed methods is also available on the Comprehensive R Archive Network. National Science Foundation (U.S.) (Grant DMS-1005539) 2018-03-19T17:51:15Z 2018-03-19T17:51:15Z 2017-02 2013-06 2018-02-16T19:01:33Z Article http://purl.org/eprint/type/JournalArticle 1935-7524 http://hdl.handle.net/1721.1/114214 Liu, Han, and Lie Wang. “TIGER: A Tuning-Insensitive Approach for Optimally Estimating Gaussian Graphical Models.” Electronic Journal of Statistics 11, 1 (February 2017): 241–294 © 2017 Institute of Mathematical Statistics https://orcid.org/0000-0003-3582-8898 http://dx.doi.org/10.1214/16-EJS1195 Electronic Journal of Statistics Attribution 2.5 Generic (CC BY 2.5) https://creativecommons.org/licenses/by/2.5/ application/pdf Institute of Mathematical Statistics Electronic Journal of Statistics |
| spellingShingle | Liu, Han Wang, Lie TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title | TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title_full | TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title_fullStr | TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title_full_unstemmed | TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title_short | TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models |
| title_sort | tiger a tuning insensitive approach for optimally estimating gaussian graphical models |
| url | http://hdl.handle.net/1721.1/114214 https://orcid.org/0000-0003-3582-8898 |
| work_keys_str_mv | AT liuhan tigeratuninginsensitiveapproachforoptimallyestimatinggaussiangraphicalmodels AT wanglie tigeratuninginsensitiveapproachforoptimallyestimatinggaussiangraphicalmodels |