English

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

R2 v1 2026-06-23T20:57:49.095Z