|
|||||
 |
|
|
|
|
|
|
Toric invariant
theory for maximum likelihood estimation in log-linear
models
Carlos Améndola, Kathlén Kohn, Philipp Reichenbach and Anna Seigal |
|
Vol. 12 (2021), No. 2, 187–211
|
|
DOI: 10.2140/astat.2021.12.187
|
Abstract |
|
We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We use notions of stability under a torus action to characterize the existence of the maximum likelihood estimate, and discuss connections to scaling algorithms. |
Keywords
maximum likelihood estimation, log-linear models, graphical
models, torus actions, null cone, scaling algorithms
|
Mathematical Subject Classification
Primary: 14L24, 20G45, 62F10, 62H22, 62R01
|
Milestones
Received: 29 January 2021
Revised: 28 July 2021
Accepted: 27 September 2021
Published: 13 December 2021
|
Authors |
| Carlos Améndola | |
| Department of Mathematics Technical University of Munich Germany |
|
| Kathlén Kohn | |
| Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden |
|
| Philipp Reichenbach | |
| Institut für Mathematik Technische Universität Berlin Germany |
|
| Anna Seigal | |
| Mathematical Institute University of Oxford United Kingdom |
Department of Mathematics Harvard University Cambridge, MA United States |
