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The maximum likelihood degree of sparse polynomial systems

Algebraic Geometry 2022-04-20 v2 Statistics Theory Statistics Theory

Abstract

We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.

Keywords

Cite

@article{arxiv.2105.07449,
  title  = {The maximum likelihood degree of sparse polynomial systems},
  author = {Julia Lindberg and Nathan Nicholson and Jose Israel Rodriguez and Zinan Wang},
  journal= {arXiv preprint arXiv:2105.07449},
  year   = {2022}
}

Comments

13 pages

R2 v1 2026-06-24T02:09:20.739Z