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Probabilistic circuits (PCs) are a prominent representation of probabilitydistributions with tractable inference. While parameter learning in PCs isrigorously studied, structure learning is often more based on heuristics thanon principled objectives. In this paper, we develop Bayesian structure scoresfor deterministic PCs, i.e., the structure likelihood with parametersmarginalized out, which are well known as rigorous objectives for structurelearning in probabilistic graphical models. When used within a greedy cutsetalgorithm, our scores effectively protect against overfitting and yield a fastand almost hyper-parameter-free structure learner, distinguishing it fromprevious approaches. In experiments, we achieve good trade-offs betweentraining time and model fit in terms of log-likelihood. Moreover, theprincipled nature of Bayesian scores unlocks PCs for accommodating frameworkssuch as structural expectation-maximization.

Bayesian Structure Scores for Probabilistic Circuits