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arXiv · 2012.00198

The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices

Carlos Améndola·Lukas Gustafsson·Kathlén Kohn·Orlando Marigliano·Anna Seigal
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Abstract

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 Schubert calculus, 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.

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Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, Orlando Marigliano, Anna Seigal. 2020-12-01. The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices. https://arxiv.org/abs/2012.00198

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