Frobenius Manifold Structure of Gaussian Maximum-Likelihood Concentration Cones
A geometric analysis showing that the positive-definite cone underlying Gaussian linear concentration models is an elliptic Monge-Ampere domain whose log-likelihood is its Hessian potential, and that the diagonal-matrix spectrahedron parametrizing such models satisfies the WDVV associativity equations, so it is a Frobenius manifold compactifying to a permutohedral toric variety. The maximum-likelihood degree is then indexed by 'Frobenius residuals', components of that compactification built from Bialynicki-Birula cells.
MAXIMUM LIKELIHOOD, PERMUTOHEDRA AND ASSOCIATIVITY EQUATIONS NO´EMIE C. COMBE Abstract. We consider
This paper studies the cone of concentration matrices of Gaussian linear concentration models, and the associated Wishart laws, from the viewpoint of algebraic geometry and information geometry. Its …