Squared Linear Models
Commutative Algebra
2025-10-21 v2 Algebraic Geometry
Statistics Theory
Statistics Theory
Abstract
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one critical point in each region of the projective hyperplane arrangement defined by the linear forms. We examine the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the MLE, we describe the log-normal polytopes, and we explore connections to determinantal point processes.
Cite
@article{arxiv.2505.19351,
title = {Squared Linear Models},
author = {Hannah Friedman and Bernd Sturmfels and Maximilian Wiesmann},
journal= {arXiv preprint arXiv:2505.19351},
year = {2025}
}
Comments
21 pages, 3 figures