Estimation of Monge matrices
© 2020 ISI/BS. Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statis...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Bernoulli Society for Mathematical Statistics and Probability
2021
|
| Online Access: | https://hdl.handle.net/1721.1/134434 |
| _version_ | 1811090821679677440 |
|---|---|
| author | Hütter, Jan-Christian Mao, Cheng Rigollet, Philippe Robeva, Elina |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hütter, Jan-Christian Mao, Cheng Rigollet, Philippe Robeva, Elina |
| author_sort | Hütter, Jan-Christian |
| collection | MIT |
| description | © 2020 ISI/BS. Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statistical estimation. In this work, we propose to view this structure as a shape constraint and study the problem of estimating a Monge matrix subject to additive random noise. More specifically, we establish the minimax rates of estimation of Monge and pre-Monge matrices. In the case of pre-Monge matrices, the minimax-optimal least-squares estimator is not efficiently computable, and we propose two efficient estimators and establish their rates of convergence. Our theoretical findings are supported by numerical experiments. |
| first_indexed | 2024-09-23T14:52:29Z |
| format | Article |
| id | mit-1721.1/134434 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:52:29Z |
| publishDate | 2021 |
| publisher | Bernoulli Society for Mathematical Statistics and Probability |
| record_format | dspace |
| spelling | mit-1721.1/1344342023-12-19T20:38:06Z Estimation of Monge matrices Hütter, Jan-Christian Mao, Cheng Rigollet, Philippe Robeva, Elina Massachusetts Institute of Technology. Department of Mathematics © 2020 ISI/BS. Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statistical estimation. In this work, we propose to view this structure as a shape constraint and study the problem of estimating a Monge matrix subject to additive random noise. More specifically, we establish the minimax rates of estimation of Monge and pre-Monge matrices. In the case of pre-Monge matrices, the minimax-optimal least-squares estimator is not efficiently computable, and we propose two efficient estimators and establish their rates of convergence. Our theoretical findings are supported by numerical experiments. 2021-10-27T20:04:59Z 2021-10-27T20:04:59Z 2020 2021-05-26T13:47:04Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134434 en 10.3150/20-BEJ1215 Bernoulli Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Bernoulli Society for Mathematical Statistics and Probability arXiv |
| spellingShingle | Hütter, Jan-Christian Mao, Cheng Rigollet, Philippe Robeva, Elina Estimation of Monge matrices |
| title | Estimation of Monge matrices |
| title_full | Estimation of Monge matrices |
| title_fullStr | Estimation of Monge matrices |
| title_full_unstemmed | Estimation of Monge matrices |
| title_short | Estimation of Monge matrices |
| title_sort | estimation of monge matrices |
| url | https://hdl.handle.net/1721.1/134434 |
| work_keys_str_mv | AT hutterjanchristian estimationofmongematrices AT maocheng estimationofmongematrices AT rigolletphilippe estimationofmongematrices AT robevaelina estimationofmongematrices |