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Toric invariant
theory for maximum likelihood estimation in log-linear
models
Carlos Améndola, Kathlén Kohn, Philipp Reichenbach and Anna Seigal |
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Vol. 12 (2021), No. 2, 187–211
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DOI: 10.2140/astat.2021.12.187
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Abstract |
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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. |
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Keywords
maximum likelihood estimation, log-linear models, graphical
models, torus actions, null cone, scaling algorithms
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Mathematical Subject Classification
Primary: 14L24, 20G45, 62F10, 62H22, 62R01
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Milestones
Received: 29 January 2021
Revised: 28 July 2021
Accepted: 27 September 2021
Published: 13 December 2021
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Authors |
| Carlos Améndola | |
| Department of Mathematics Technical University of Munich Germany |
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| Kathlén Kohn | |
| Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden |
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| Philipp Reichenbach | |
| Institut für Mathematik Technische Universität Berlin Germany |
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| Anna Seigal | |
| Mathematical Institute University of Oxford United Kingdom |
Department of Mathematics Harvard University Cambridge, MA United States |
