Methods and systems are disclosed for learning Bayesian networks. The approach is based on specifying a search space that enables searching over equivalence classes of the Bayesian network. A set of one or more operators are applied to a representation of the equivalence class. A suitable search algorithm searches in the search space by scoring the operators locally with a decomposable scoring criteria. To facilitate application of the operators and associated scoring, validity tests can be performed to determine whether a given operator is valid relative to the current state representation.