Date: 29 April, 2020. Kolkata time 8:00 pm (= UTC + 5:30)
SEMINAR SERIES ON RECENT PROGRESS IN GEOMETRIC COMPLEXITY THEORY
Zoom Meeting Id: 87525612114
Torus Actions and Maximum Likelihood Estimation
University of Oxford.
We describe connections between invariant theory and maximum likelihood estimation, in the context of log-linear models. Finding a maximum likelihood estimate (MLE) is an optimisation problem over a statistical model, to obtain the point that best fits observed data. We show that this is equivalent to a capacity problem - finding the point of minimal norm in an orbit under a corresponding torus action. The existence of the MLE can then be characterized by stability under the action. Moreover, algorithms from statistics can be used in invariant theory, and vice versa. Based on joint work with Carlos Améndola, Kathlén Kohn and Philipp Reichenbach.