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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
108/2020

Reciprocal maximum likelihood degrees of diagonal linear concentration models

Christopher Eur, Tara Fife, José Alejandro Samper and Tim Seynnaeve

Abstract

We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model $\mathcal L \subseteq \mathbb{C}^n$ of dimension $r$ is equal to $$(-2)^r\chi_M( \textstyle\frac{1}{2}),$$where $\chi_M$ is the characteristic polynomial of the matroid $M$ associated to $\mathcal L$.

In particular, this establishes the polynomiality of the rmld for general diagonal linear concentration models, positively answering a question of Sturmfels, Timme, and Zwiernik.

Received:
Dec 2, 2020
Published:
Dec 2, 2020
Keywords:
maximum likelihood degrees, reciprocal spaces, matroids, characteristic polynomials

Related publications

inJournal
2021 Journal Open Access
Christopher Eur, Tara Fife, Jose Alejandro Samper and Tim Seynnaeve

Reciprocal maximum likelihood degrees of diagonal linear concentration models

In: Le Matematiche, 76 (2021) 2, pp. 447-459