Journal article
The maximum likelihood degree of linear spaces of symmetric matrices
- 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 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 324.1KB, Terms of use)
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- Publisher copy:
- 10.4418/2021.76.2.15
Authors
- Publisher:
- Dipartimento di Matematica e Informatica, University of Catania
- Journal:
- Le Matematiche More from this journal
- Volume:
- 76
- Issue:
- 2
- Pages:
- 535–557
- Place of publication:
- Catania, Italy
- Publication date:
- 2021-10-10
- Acceptance date:
- 2021-05-15
- DOI:
- ISSN:
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0373-3505
- Language:
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English
- Keywords:
- Pubs id:
-
1176462
- Local pid:
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pubs:1176462
- Deposit date:
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2021-05-15
Terms of use
- Copyright holder:
- Améndola et al
- Copyright date:
- 2021
- Rights statement:
- Copyright © 2021 Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, Orlando Marigliano, Anna Seigal Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License. The authors retain all rights to the original work without any restrictions.
- Licence:
- CC Attribution (CC BY)
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