@article{1092, abstract = {A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. We show that there is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models we give a construction of this polytope as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models. }, author = {Mohammadi, Fatemeh and Uhler, Caroline and Wang, Charles and Yu, Josephine}, journal = {SIAM Journal on Discrete Mathematics}, number = {1}, pages = {64--93}, publisher = {SIAM}, title = {{Generalized permutohedra from probabilistic graphical models}}, doi = {10.1137/16M107894X}, volume = {32}, year = {2018}, }