The present invention leverages scalable learning methods to efficiently obtain a Bayesian network for a set of variables of which the total ordering in a domain is known. Certain criteria are employed to generate a Bayesian network which is then evaluated and utilized as a guide to generate another Bayesian network for the set of variables. Successive iterations are performed utilizing a prior Bayesian network as a guide until a stopping criterion is reached, yielding a best-effort Bayesian network for the set of variables.