Structure learning in Bayesian Networks using regular vines

Learning the structure of a Bayesian Network from multidimensional data is an important task in many situations, as it allows understanding conditional (in)dependence relations which in turn can be used for prediction. Current methods mostly assume a multivariate normal or a discrete multinomial model. A new greedy learning algorithm for continuous non-Gaussian variables, where marginal distributions can be arbitrary, as well as the dependency structure, is proposed. It exploits the regular vine approximation of the model, which is a tree-based hierarchical construction with pair-copulae as building blocks. It is shown that the networks obtainable with our algorithm belong to a certain subclass of chordal graphs. Chordal graphs representations are often preferred, as they allow very efficient message passing and information propagation in intervention studies. It is illustrated through several examples and real data applications that the possibility of using non-Gaussian margins and a non-linear dependency structure outweighs the restriction to chordal graphs.