Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective

@article{Sattelberger2021MaximumLE,
  title={Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective},
  author={Anna-Laura Sattelberger and Robin van der Veer},
  journal={arXiv: Algebraic Geometry},
  year={2021}
}
In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their asymptotic behavior. We relate these asymptotics to particular rays in the tropical variety as well as to Bernstein--Sato ideals and give a connection to Maximum Likelihood Estimation in Statistics. 
Nonlinear Algebra and Applications
TLDR
This review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraIC vision, and tensor decompositions.

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