Invariant theory and scaling algorithms for maximum likelihood estimation
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical models given by transitive directed acyclic graphs. We use...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics
2021
|
| _version_ | 1797056302182039552 |
|---|---|
| author | Améndola, C Kohn, K Reichenbach, P Seigal, AL |
| author_facet | Améndola, C Kohn, K Reichenbach, P Seigal, AL |
| author_sort | Améndola, C |
| collection | OXFORD |
| description | We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical models given by transitive directed acyclic graphs. We use stability under group actions to characterize boundedness of the likelihood, and existence and uniqueness of the maximum likelihood estimate. Our approach reveals promising consequences of the interplay between invariant theory and statistics. In particular, existing scaling algorithms from statistics can be used in invariant theory, and vice versa. |
| first_indexed | 2024-03-06T19:21:28Z |
| format | Journal article |
| id | oxford-uuid:1a3ca0e9-4c89-4197-81cf-cd2e570c287b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:21:28Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:1a3ca0e9-4c89-4197-81cf-cd2e570c287b2022-03-26T10:53:39ZInvariant theory and scaling algorithms for maximum likelihood estimationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1a3ca0e9-4c89-4197-81cf-cd2e570c287bEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2021Améndola, CKohn, KReichenbach, PSeigal, ALWe uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical models given by transitive directed acyclic graphs. We use stability under group actions to characterize boundedness of the likelihood, and existence and uniqueness of the maximum likelihood estimate. Our approach reveals promising consequences of the interplay between invariant theory and statistics. In particular, existing scaling algorithms from statistics can be used in invariant theory, and vice versa. |
| spellingShingle | Améndola, C Kohn, K Reichenbach, P Seigal, AL Invariant theory and scaling algorithms for maximum likelihood estimation |
| title | Invariant theory and scaling algorithms for maximum likelihood estimation |
| title_full | Invariant theory and scaling algorithms for maximum likelihood estimation |
| title_fullStr | Invariant theory and scaling algorithms for maximum likelihood estimation |
| title_full_unstemmed | Invariant theory and scaling algorithms for maximum likelihood estimation |
| title_short | Invariant theory and scaling algorithms for maximum likelihood estimation |
| title_sort | invariant theory and scaling algorithms for maximum likelihood estimation |
| work_keys_str_mv | AT amendolac invarianttheoryandscalingalgorithmsformaximumlikelihoodestimation AT kohnk invarianttheoryandscalingalgorithmsformaximumlikelihoodestimation AT reichenbachp invarianttheoryandscalingalgorithmsformaximumlikelihoodestimation AT seigalal invarianttheoryandscalingalgorithmsformaximumlikelihoodestimation |