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The problem of learning Markov equivalence classes of Bayesian networkstructures may be solved by searching for the maximum of a scoring metric in aspace of these classes. This paper deals with the definition and analysis ofone such search space. We use a theoretically motivated neighbourhood, theinclusion boundary, and represent equivalence classes by essential graphs. Weshow that this search space is connected and that the score of the neighbourscan be evaluated incrementally. We devise a practical way of building thisneighbourhood for an essential graph that is purely graphical and does notexplicitely refer to the underlying independences. We find that its size can beintractable, depending on the complexity of the essential graph of theequivalence class. The emphasis is put on the potential use of this space withgreedy hill -climbing search

On the Construction of the Inclusion Boundary Neighbourhood for Markov Equivalence Classes of Bayesian Network Structures