Maximum likelihood degree and space of orbits of a C^* action
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We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on a smooth compact moduli space of orbits of a C^* action on the Lagrangian Grassmannian which we call Gaussian moduli. This allows us to provide an explicit, basic, albeit of high computational complexity, formula for the ML-degree. The Gaussian moduli is an exact analog for symmetric matrices of the permutohedron variety for the diagonal matrices.
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