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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. Thisis a joint work with Fatemeh Mohammadi, Caroline Uhler, and Charles Wang.

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