Drton–Sturmfels–Sullivant conjecture on the ML-degree of cycle graphs

From papers

Let CnC_n be the cycle graph on nn vertices, and let \MLdeg(Cn)\MLdeg(C_n) denote the number of critical points of the Gaussian log-likelihood function for generic sample covariance data, equivalently the maximum likelihood degree of the corresponding Gaussian graphical model. Drton–Sturmfels–Sullivant conjecture.

\MLdeg(Cn)=(n3)2n2+1.\MLdeg(C_n)=(n-3)\cdot 2^{n-2}+1.

This conjecture predicts the observed ML-degrees of cycle graphs and gives an explicit formula for their algebraic statistical complexity. The supplied text does not state whether the conjecture has been proved or disproved.

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Primary source

Carlos Améndola, Rodica Andreea Dinu, Mateusz Michałek and Martin Vodička, “On the maximum likelihood degree for Gaussian graphical models”, arXiv:2410.07007 (2024).

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