Learning Bounded Treewidth Bayesian Networks

With the increased availability of data for complex domains, it is desirable to learn Bayesian network structures that are sufficiently expressive for generalization while at the same time allow for tractable inference. While the method of thin junction trees can, in principle, be used for this purpose, its fully greedy nature makes it prone to overfitting, particularly when data is scarce. In this work we present a novel method for learning Bayesian networks of bounded treewidth that employs global structure modifications and that is polynomial both in the size of the graph and the treewidth bound. At the heart of our method is a dynamic triangulation that we update in a way that facilitates the addition of chain structures that increase the bound on the model's treewidth by at most one. We demonstrate the effectiveness of our "treewidth-friendly" method on several real-life data sets and show that it is superior to the greedy approach as soon as the bound on the treewidth is nontrivial. Importantly, we also show that by making use of global operators, we are able to achieve better generalization even when learning Bayesian networks of unbounded treewidth.