An Algebraic Characterization of Equivalent Bayesian Networks

In this paper, we propose an algebraic characterization for equivalent classes of Bayesian networks. Unlike the other characterizations, which are based on the graphical structure of Bayesian networks, our algebraic characterization is derived from the intrinsic algebraic structure of Bayesian networks, i.e., joint probability distribution factorization. The new proposed algebraic characterization not only provides us with a new perspective to look into equivalent Bayesian networks, but also suggests simple and efficient methods for determining equivalence of Bayesian networks and identifying compelled edges in Bayesian networks.