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arXiv 2011.141822020-11math.STmath.AGmath.COstat.TH

Reciprocal maximum likelihood degrees of diagonal linear concentration models

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

备注：: 13 pages, comments welcome To appear in: Le Matematiche, vol. 76 (2) (special issue on Linear Spaces of Symmetric Matrices)

英文摘要：

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 $(-2)^rχ_M( \textstyle\frac{1}{2})$, where $χ_M$ 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.

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