Toric invariant theory for maximum likelihood estimation in log-linear models

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.

This is a companion paper to arXiv:2003.13662. v2: referee comments worked in, added appendices A and B

References in corpus (2)

• On the toric algebra of graphical models
• Interior-point methods for unconstrained geometric programming and scaling problems

Cited by in corpus (3)

• Interior-point methods on manifolds: theory and applications
• Rational partition models under iterative proportional scaling
• Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks