Information, Geometry, and Physics Seminar

I will revisit the problem of maximizing information divergence from a new perspective using logarithmic Voronoi polytopes. We will see that for linear models, the maximum is always achieved at the boundary of the probability simplex. For toric models, I will describe an algorithm that combines the combinatorics of the chamber complex with numerical algebraic geometry. I will pay special attention to reducible models and models of maximum likelihood degree one, with many colorful examples. This talk is based on joint work with Serkan Hoşten.