Commutative Algebra and Algebraic Geometry: The maximum likelihood degree of a toric variety

Seminar | March 7 | 3:45-4:45 p.m. | 939 Evans Hall

 Serkan Hosten, San Francisco State University

 Department of Mathematics

The maximum likelihood degree (ML degree) of a projective variety is the number of complex critical points of the likelihood function with generic data. We consider the ML degree of projective toric varieties. For this, we look at "scaled" toric varieties given by a monomial parametrization involving arbitrary complex coefficients. We show that for generic choice of coefficients the ML degree of such a scaled toric variety is equal to the degree of the original toric variety. We also prove that the ML degree drops if and only if the scaling vector is on the hypersurface defined by the principal A-determinant. With this tool in our hand, we will compute the ML degree of various classical toric varieties, of toric hypersurfaces, and toric varieties arising in graphical models.