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 the Bayesian network, our algebraic characterization is derived from its intrinsic algebraic structure, i.e., the factorization of its joint probability distribution. 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.
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