Learning Binary Bayesian Networks in Polynomial Time and Sample Complexity.

We consider the problem of structure learning for binary Bayesian networks. Our approach is to recover the true parents and children for each node first and then combine the results to recover the skeleton. We do not assume any specific conditional probability distribution for the nodes. Rather, we show that if the expectations of products of node pairs satisfy certain conditions then we can do exact recovery of parents and children of a node by performing l_1-regularized linear regression with sufficient number of samples. The sample complexity of our proposed approach depends logarithmically on number of nodes in the Bayesian network. Furthermore, our method runs in polynomial time.