A Transformational Characterization of Equivalent Bayesian Network Structures

We present a simple characterization of equivalent Bayesian network structures based on local transformations. The sig­ nificance of the characterization is twofold. First, we are able to easily prove several new invariant properties of theoretical in­ terest for equivalent structures. Second, we use the characterization to derive an ef­ ficient algorithm that identifies all of the compelled edges in a structure. Compelled edge identification is of particular impor­ tance for learning Bayesian network struc­ tures from data because these edges indi­ cate causal relationships when certain as­ sumptions hold.