Reciprocal maximum likelihood degrees of diagonal linear concentration models

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

Contact the author: Please use for correspondence this email.
Submission date: 02. Dec. 2020
Pages: 15
Bibtex
Keywords and phrases: maximum likelihood degrees, reciprocal spaces, matroids, characteristic polynomials
Download full preprint: PDF (162 kB)
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model ℒ⊆ ℂⁿ of dimension r is equal to (−2)^rχ_M(), where χ_M is the characteristic polynomial of the matroid M associated to 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.