The maximum likelihood degree of linear spaces of symmetric matrices
C Am�ndola, L Gustafsson, K Kohn…�- arXiv preprint arXiv�…, 2020 - arxiv.org
arXiv preprint arXiv:2012.00198, 2020•arxiv.org
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.
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.
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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