Random Probabilistic Circuits

Density estimation could be viewed as a core component in machine learning, since a good estimator could be used to solve many tasks such as classification, regression, and imputing missing values. The main challenge of density estimation is balancing the model expressiveness and its learning and inference complexity. Probabilistic circuits (PCs) model a probability distribution as a computational graph. By imposing specific structural properties on such models many inference tasks become tractable. However, learning PCs usually relies on greedy and time consuming algorithms. In this paper we propose a new unified approach to efficiently learn PCs having several structural properties. We introduce extremely randomized PCs (XPCs), PCs with a random structure. We show their advantage on standard density estimation benchmarks when compared to other density estimators.