Brownian motion tree models are toric
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic char-acterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Information Theory and Automation
2022
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| Online Access: | https://hdl.handle.net/1721.1/143914 |
| _version_ | 1811071773337190400 |
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| author | Sturmfels, Bernd Uhler, Caroline Zwiernik, Piotr |
| 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 Sturmfels, Bernd Uhler, Caroline Zwiernik, Piotr |
| author_sort | Sturmfels, Bernd |
| collection | MIT |
| description | Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic char-acterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum likelihood estimation. Our results also give new insights into the geometry of ultrametric matrices. |
| first_indexed | 2024-09-23T08:56:00Z |
| format | Article |
| id | mit-1721.1/143914 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:56:00Z |
| publishDate | 2022 |
| publisher | Institute of Information Theory and Automation |
| record_format | dspace |
| spelling | mit-1721.1/1439142023-03-28T19:42:53Z Brownian motion tree models are toric Sturmfels, Bernd Uhler, Caroline Zwiernik, Piotr Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Institute for Data, Systems, and Society Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic char-acterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum likelihood estimation. Our results also give new insights into the geometry of ultrametric matrices. 2022-07-21T13:35:46Z 2022-07-21T13:35:46Z 2021 2022-07-21T13:24:34Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/143914 Sturmfels, Bernd, Uhler, Caroline and Zwiernik, Piotr. 2021. "Brownian motion tree models are toric." Kybernetika, 56 (6). en 10.14736/KYB-2020-6-1154 Kybernetika Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Information Theory and Automation arXiv |
| spellingShingle | Sturmfels, Bernd Uhler, Caroline Zwiernik, Piotr Brownian motion tree models are toric |
| title | Brownian motion tree models are toric |
| title_full | Brownian motion tree models are toric |
| title_fullStr | Brownian motion tree models are toric |
| title_full_unstemmed | Brownian motion tree models are toric |
| title_short | Brownian motion tree models are toric |
| title_sort | brownian motion tree models are toric |
| url | https://hdl.handle.net/1721.1/143914 |
| work_keys_str_mv | AT sturmfelsbernd brownianmotiontreemodelsaretoric AT uhlercaroline brownianmotiontreemodelsaretoric AT zwiernikpiotr brownianmotiontreemodelsaretoric |