Efficient Sampling and Structure Learning of Bayesian Networks

Abstract

Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high-dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks in combination with the acyclicity constraint. Efforts have focused on two fronts: constraint-based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. Here, we synthesize these two fields in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint-based method. Individual steps in the MCMC scheme only require simple table lookups so that very long chains can be efficiently obtained. Furthermore, the scheme includes an iterative procedure to correct for errors from the conditional independence tests. The algorithm offers markedly superior performance to alternatives, particularly because it also offers the possibility to sample DAGs from their posterior distribution, enabling full Bayesian model averaging for much larger Bayesian networks. Supplementary materials for this article are available online.