Sum-product networks (SPNs) are rooted, directed acyclic graphs (DAGs) of sum and product nodes with well-defined probabilistic semantics. Moreover, exact inference in the distribution represented by an SPN is guaranteed to take linear time in the size of the DAG. In this paper we introduce an algorithm that learns the structure of an SPN using a greedy search approach. It incorporates methods used in a previous SPN structure-learning algorithm, but, unlike the previous algorithm, is not limited to learning tree-structured SPNs. Several proven ideas from circuit complexity theory along with our experimental results provide evidence for the advantages of SPNs with less-restrictive, non-tree structures.

The sum-product network (SPN) is a recently-proposed deep model consisting of a network of sum and product nodes, and has been shown to be competitive with state-of-the-art deep models on certain difficult tasks such as image completion. Designing an SPN network architecture that is suitable for the task at hand is an open question. We propose an algorithm for learning the SPN architecture from data. The idea is to cluster variables (as opposed to data instances) in order to identify variable subsets that strongly interact with one another. Nodes in the SPN network are then allocated towards explaining these interactions. Experimental evidence shows that learning the SPN architecture significantly improves its performance compared to using a previously-proposed static architecture.