Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation

We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit invariant theory. focus on Gaussian transformation families, which include matrix normal models graphical given by transitive directed acyclic graphs. use stability under actions to characterize boundedness of the likelihood, existence uniqueness estimate. Our approach reveals promising consequences interplay theory statistics. In particular, existing scaling algorithms from can be used theory, vice versa.