Probabilistic Circuits with Constraints via Convex Optimization
Soroush Ghandi Benjamin Quost Cassio de Campos
This work addresses integrating probabilistic propositional logic constraints
into the distribution encoded by a probabilistic circuit (PC). PCs are a class
of tractable models that allow efficient computations (such as conditional and
marginal probabilities) while achieving state-of-the-art performance in some
domains. The proposed approach takes both a PC and constraints as inputs, and
outputs a new PC that satisfies the constraints. This is done efficiently via
convex optimization without the need to retrain the entire model. Empirical
evaluations indicate that the combination of constraints and PCs can have
multiple use cases, including the improvement of model performance under scarce
or incomplete data, as well as the enforcement of machine learning fairness
measures into the model without compromising model fitness. We believe that
these ideas will open possibilities for multiple other applications involving
the combination of logics and deep probabilistic models.