Maximum Likelihood Degree, Complete Quadrics, and C*-Action

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2021
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Monin, Leonid
Wiśniewski, Jarosław A.
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SIAM Journal on Applied Algebra and Geometry. Society for Industrial and Applied Mathematics (SIAM). 2021, 5(1), pp. 60-85. eISSN 2470-6566. Available under: doi: 10.1137/20M1335960
Zusammenfassung

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit and basic, albeit very computationally complex, formula for the ML-degree. The variety of complete quadrics is an exact analogue for symmetric matrices of the permutohedron variety for the diagonal matrices.

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ISO 690MICHALEK, Mateusz, Leonid MONIN, Jarosław A. WIŚNIEWSKI, 2021. Maximum Likelihood Degree, Complete Quadrics, and C*-Action. In: SIAM Journal on Applied Algebra and Geometry. Society for Industrial and Applied Mathematics (SIAM). 2021, 5(1), pp. 60-85. eISSN 2470-6566. Available under: doi: 10.1137/20M1335960
BibTex
@article{Michalek2021Maxim-53381,
  year={2021},
  doi={10.1137/20M1335960},
  title={Maximum Likelihood Degree, Complete Quadrics, and C*-Action},
  number={1},
  volume={5},
  journal={SIAM Journal on Applied Algebra and Geometry},
  pages={60--85},
  author={Michalek, Mateusz and Monin, Leonid and Wiśniewski, Jarosław A.}
}
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