Carlos Améndola Cerón: Likelihood Geometry of Correlation Models

Abstract

Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. In this talk we will consider the fascinating geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix, the Stein's loss and the symmetrized Stein's loss, which lead naturally to the algebraic statistical concepts of dual ML degree and SSL degree. I will also present exciting open problems in this direction. This is joint work with Piotr Zwiernik.