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Publication - Dr Fatemeh Mohammadi

    Generalized permutohedra from probabilistic graphical models


    Mohammadi, F, Uhler, C, Wang, C & Yu, J, 2018, ‘Generalized permutohedra from probabilistic graphical models’. SIAM Journal on Discrete Mathematics, vol 32., pp. 64-93


    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. 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 and also for mixed graphical models containing undirected, directed, and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, 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.

    Full details in the University publications repository