Scaling up the Greedy Equivalence Search algorithm by constraining the search space of equivalence classes

Greedy Equivalence Search (GES) is nowadays the state of the art algorithm for learning Bayesian networks (BNs) from complete data. However, from a practical point of view, this algorithm may not be efficient enough to deal with data from high dimensionality and/or complex domains. This paper proposes some modifications to GES aimed at increasing its efficiency. Under the faithfulness assumption, the modified algorithms preserve the same theoretical properties of the original one, that is, they recover a perfect map of the target distribution in the large sample limit. Moreover, experimental results confirm that, although the proposed methods carry out a significantly smaller number of computations, the quality of the BNs learned can be compared with those obtained with GES.

► We propose nine variants to Greedy Equivalence Search (GES).
► We proved that seven of the proposed algorithms are asymptotically optimal.
► Some of the algorithms are comparable to GES in terms of accuracy.
► Results confirm that the proposed algorithms are more efficient than GES.