The Maximum Likelihood Degree of Sparse Polynomial Systems
Julia Lindberg, Nathan Nicholson, Jose Israel Rodriguez, Zinan Wang · SIAM Journal on Applied Algebra and Geometry · 2023
Abstract. We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood (ML) degree counts the number of critical points of the likelihood function restricted to the model. We prove that the ML degree of a generic sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.