Imposing Constraints in Probabilistic Circuits via Gradient Optimization

Soroush Ghandi, Benjamin Quost, Cassio de Campos

Abstract: Probabilistic Circuits (PCs) are a class of tractable models that allow a range of efficient and exact computations while achieving state-of-the-art performance in some domains. In this work, we propose a sample-based procedure to let the distribution encoded by a PC satisfy probabilistic propositional logic constraints. This sample-based method is proposed as a direct competitor to a mathematical approach previously introduced, which is based on optimizing a convex upper bound of the KL divergence. In our empirical study, we compare both methods in two different scenarios, where constraints are utilized to: i) apply fairness to a distribution; and ii) improve the performance of a PC model under scarce data. Our results indicate that although both methods are competitive to one another in the case of fairness, sample-based method has an advantage in scenarios with scarce data.