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We introduce Selective Greedy Equivalence Search (SGES), a restricted versionof Greedy Equivalence Search (GES). SGES retains the asymptotic correctness ofGES but, unlike GES, has polynomial performance guarantees. In particular, weshow that when data are sampled independently from a distribution that isperfect with respect to a DAG ${\cal G}$ defined over the observable variablesthen, in the limit of large data, SGES will identify ${\cal G}$'s equivalenceclass after a number of score evaluations that is (1) polynomial in the numberof nodes and (2) exponential in various complexity measures includingmaximum-number-of-parents, maximum-clique-size, and a new measure called {\emv-width} that is at least as small as---and potentially much smaller than---theother two. More generally, we show that for any hereditary andequivalence-invariant property $\Pi$ known to hold in ${\cal G}$, we retain thelarge-sample optimality guarantees of GES even if we ignore any GES deletionoperator during the backward phase that results in a state for which $\Pi$ doesnot hold in the common-descendants subgraph.

Selective Greedy Equivalence Search: Finding Optimal Bayesian Networks Using a Polynomial Number of Score Evaluations