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Philipp Reichenbach
- © Philipp Reichenbach
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin Büro
Raum MA 319 (3. OG)
Institut für Mathematik Persönliche Homepage:
page.math.tu-berlin.de/~reichenb/ ORCiD
0000-0002-5722-5505
Publikationen in der Arbeitsgruppe
| Citation key | AKRS-InvariantTheoryAndScalingAlgorithmsForMaximumLikelihoodEstimation |
|---|---|
| Author | Carlos Améndola and Kathlén Kohn and Philipp Reichenbach and Anna Seigal |
| Year | 2020 |
| Month | 3 |
| Abstract | 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. |
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