Learning Sum-Product Networks with Direct and Indirect Variable Interactions

Sum-product networks (SPNs) are a deep probabilistic representation that allows for efficient, exact inference. SPNs generalize many other tractable models, including thin junction trees, latent tree models, and many types of mixtures. Previous work on learning SPN structure has mainly focused on using top-down or bottom-up clustering to find mixtures, which capture variable interactions indirectly through implicit latent variables. In contrast, most work on learning graphical models, thin junction trees, and arithmetic circuits has focused on finding direct interactions among variables. In this paper, we present ID-SPN, a new algorithm for learning SPN structure that unifies the two approaches. In experiments on 20 benchmark datasets, we find that the combination of direct and indirect interactions leads to significantly better accuracy than several state-of-the-art algorithms for learning SPNs and other tractable models.