Learning Bayesian Networks Using Generalized Permutohedra
Fatemeh Mohammadi (University of Bristol)
Friday 11th May, 2018 15:00-16:00 Seminar room 311B
Abstract
Graphical models (Bayesian networks) based on directed acyclic graphs (DAGs) are used to model complex cause-and-effect systems. A graphical model is a family of joint probability distributions over the nodes of a graph which encodes conditional independence relations via the Markov properties. One of the fundamental problems in causality is to learn an unknown graph based on a set of observed conditional independence relations. In this talk, I will describe a greedy algorithm for DAG model selection that operate via edge walks on so-called DAG associahedra. For an undirected graph the set of 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. For any regular Gaussian model, and its associated set of conditional independence relations we construct the analogous polytope DAG associahedon which can be defined using relative entropy. For DAGs we construct this polytope as a Minkowski sum of matroid polytopes corresponding to Bayes-ball paths in graph.
This is a joint work with Caroline Uhler, Charles Wang, and Josephine Yu.
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