Learning the Structure of Probabilistic Sentential Decision Diagrams

The probabilistic sentential decision diagram (PSDD) was recently introduced as a tractable representation of probability distributions that are subject to logical constraints. Meanwhile, efforts in tractable learning achieved great success inducing complex joint distributions from data without constraints, while guaranteeing efficient exact probabilistic inference; for instance by learning arithmetic circuits (ACs) or sum-product networks (SPNs). This paper studies the efficacy of PSDDs for the standard tractable learning task without constraints and develops the first PSDD structure learning algorithm, called LEARNPSDD. Experiments on standard benchmarks show competitive performance, despite the fact that PSDDs are more tractable and more restrictive than their alternatives. LEARNPSDD compares favorably to SPNs, particularly in terms of model size, which is a proxy for tractability. We report state-of-the-art likelihood results on six datasets. Moreover, LEARNPSDD retains the ability to learn PSDD structures in probability spaces subject to logical constraints, which is beyond the reach of other representations.