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

Mateusz Michałek; Leonid Monin; Jarosław A. Wiśniewski

doi:10.1137/20M1335960

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

Mateusz Michałek, Leonid Monin, Jarosław A. Wiśniewski

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

22 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	60-85
Journal	SIAM Journal on Applied Algebra and Geometry
Volume	5
Issue number	1
DOIs	https://doi.org/10.1137/20M1335960
Publication status	Published - 1 Jan 2021

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10.1137/20M1335960

https://arxiv.org/abs/2004.07735

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title = "Maximum Likelihood Degree, Complete Quadrics, and C*-Action",

abstract = "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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AU - Monin, Leonid

AU - Wiśniewski, Jarosław A.

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N2 - 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.

AB - 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.

U2 - 10.1137/20M1335960

DO - 10.1137/20M1335960

M3 - Article (Academic Journal)

SN - 2470-6566

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SP - 60

EP - 85

JO - SIAM Journal on Applied Algebra and Geometry

JF - SIAM Journal on Applied Algebra and Geometry

IS - 1

ER -

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

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