Exact formulas for the normalizing constants of Wishart distributions for graphical models
© Institute of Mathematical Statistics, 2018. Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematical Statistics
2021
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| Online Access: | https://hdl.handle.net/1721.1/134197 |
| _version_ | 1826216955161346048 |
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| author | Uhler, Caroline Lenkoski, Alex Richards, Donald |
| author_facet | Uhler, Caroline Lenkoski, Alex Richards, Donald |
| author_sort | Uhler, Caroline |
| collection | MIT |
| description | © Institute of Mathematical Statistics, 2018. Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until now, it was unknown whether the normalizing constant for a general graph could be represented explicitly, and a considerable body of computational literature emerged that attempted to avoid this apparent intractability. We close this question by providing an explicit representation of the G-Wishart normalizing constant for general graphs. |
| first_indexed | 2024-09-23T16:55:49Z |
| format | Article |
| id | mit-1721.1/134197 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:55:49Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1341972022-04-01T17:10:41Z Exact formulas for the normalizing constants of Wishart distributions for graphical models Uhler, Caroline Lenkoski, Alex Richards, Donald © Institute of Mathematical Statistics, 2018. Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until now, it was unknown whether the normalizing constant for a general graph could be represented explicitly, and a considerable body of computational literature emerged that attempted to avoid this apparent intractability. We close this question by providing an explicit representation of the G-Wishart normalizing constant for general graphs. 2021-10-27T20:03:56Z 2021-10-27T20:03:56Z 2018 2019-07-09T17:51:58Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134197 en 10.1214/17-AOS1543 The Annals of Statistics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Mathematical Statistics arXiv |
| spellingShingle | Uhler, Caroline Lenkoski, Alex Richards, Donald Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title | Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title_full | Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title_fullStr | Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title_full_unstemmed | Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title_short | Exact formulas for the normalizing constants of Wishart distributions for graphical models |
| title_sort | exact formulas for the normalizing constants of wishart distributions for graphical models |
| url | https://hdl.handle.net/1721.1/134197 |
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