Maximum likelihood thresholds of generic linear concentration models
Statistics Theory
2026-05-15 v2 Algebraic Geometry
Statistics Theory
Abstract
The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear concentration models. This turns out to be the number that one might expect from a naive dimension count, which is nontrivial to prove given that the maximum likelihood threshold is a semi-algebraic concept. We also describe geometrically how a linear concentration model can fail to exhibit this generic behavior.
Cite
@article{arxiv.2305.06280,
title = {Maximum likelihood thresholds of generic linear concentration models},
author = {Daniel Irving Bernstein and Steven J. Gortler and Louis Theran},
journal= {arXiv preprint arXiv:2305.06280},
year = {2026}
}