Toric invariant theory for maximum likelihood estimation in log-linear models
Statistics Theory
2021-12-15 v2 Algebraic Geometry
Statistics Theory
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
Cite
@article{arxiv.2012.07793,
title = {Toric invariant theory for maximum likelihood estimation in log-linear models},
author = {Carlos Améndola and Kathlén Kohn and Philipp Reichenbach and Anna Seigal},
journal= {arXiv preprint arXiv:2012.07793},
year = {2021}
}
Comments
This is a companion paper to arXiv:2003.13662. v2: referee comments worked in, added appendices A and B