The Maximum Likelihood Degree Of Linear Spaces Of Symmetric Matrices

The Maximum Likelihood Degree Of Linear Spaces Of Symmetric Matrices

We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over a linear space of symmetric matrices. We obtain new formula...

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Bibliographic Details
Published in:Matematiche Vol. 76; no. 2; p. 535
Main Authors: Amendola, Carlos, Gustafsson, Lukas, Kohn, Kathlén, Marigliano, Orlando, Seigal, Anna
Format: Journal Article
Language:English
Published: 2021
Subjects:
concentration matrix
maximum likelihood degree
Multivariate Gaussian models
Segre classes
Online Access:Get full text
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Description
Summary:We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over a linear space of symmetric matrices. We obtain new formulae for the ML degree, one via line geometry, and another using Segre classes from intersection theory. We settle the case of codimension one models, and characterize the degenerate case when the ML degree is zero.
ISSN:0373-3505
2037-5298
DOI:10.4418/2021.76.2.15