Generalized Permutohedra from Probabilistic Graphical Models

A graphical model encodes conditional independence relations among random variables. For an undirected graph these conditional independence relations are represented by a simple polytope known as the graph associahedron, which is a Minkowski sum of standard simplices. We prove that there are analogous polytopes for a much larger class of graphical models.   We construct this polytope as a Minkowski sum of matroid polytopes.  The motivation came from the problem of learning Bayesian networks from observational data.  No background on graphical models will be assumed for the talk.  This is a joint work with Fatemeh Mohammadi, Caroline Uhler, and Charles Wang.