Generalized Permutohedra from Probabilistic Graphical Models

Combinatorics Seminar
Friday, February 3, 2017 - 3:05pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations are represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from any regular Gaussian model, and it can be defined using relative entropy.  For directed acyclic graphical models we give a construction of this polytope as a Minkowski sum of matroid polytopes.  The motivation came from the problem of learning Bayesian networks from observational data.  This is a joint work with Fatemeh Mohammadi, Caroline Uhler, and Charles Wang.