Invariant theory and scaling algorithms for maximum likelihood estimation
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.
Cite
@article{arxiv.2003.13662,
title = {Invariant theory and scaling algorithms for maximum likelihood estimation},
author = {Carlos Améndola and Kathlén Kohn and Philipp Reichenbach and Anna Seigal},
journal= {arXiv preprint arXiv:2003.13662},
year = {2021}
}
Comments
34 pages; The discrete part on log-linear models from version 1 is contained in the companion paper arXiv:2012.07793. (v4: very minor changes compared to v3)