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The maximum likelihood degree of sparse polynomial systems
Julia Lindberg, Nathan Nicholson, Jose Israel Rodriguez, Zinan W · 2021-05-16 · via math.ST updates on arXiv.org

We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.

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