Likelihood Degenerations
Abstract
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points is known as the maximum likelihood (ML) degree. When the variety is smooth, it coincides with the Euler characteristic. We introduce degeneration techniques that are inspired by the soft limits in CEGM theory, and we answer several questions raised in the physics literature. These pertain to bounded regions in discriminantal arrangements and to moduli spaces of point configurations. We present theory and practise, connecting complex geometry, tropical combinatorics, and numerical nonlinear algebra.
Cite
@article{arxiv.2107.10518,
title = {Likelihood Degenerations},
author = {Daniele Agostini and Taylor Brysiewicz and Claudia Fevola and Lukas Kühne and Bernd Sturmfels and Simon Telen},
journal= {arXiv preprint arXiv:2107.10518},
year = {2022}
}
Comments
33 pages, updated to reflect reviewers' comments and added link to Zenodo to certify numerical results