Generative Clausal Networks: Relational Decision Trees as Probabilistic Circuits

In many real-world applications, the i.i.d. assumption does not hold and thus capturing the interactions between instances is essential for the task at hand. Recently, a clear connection between predictive modelling such as decision trees and probabilistic circuits, a form of deep probabilistic model, has been established although it is limited to propositional data. We introduce the first connection between relational rule models and probabilistic circuits, obtaining tractable inference from discriminative rule models while operating on the relational domain. Specifically, given a relational rule model, we make use of Mixed Sum-Product Networks (MSPNs)—a deep probabilistic architecture for hybrid domains—to equip them with a full joint distribution over the class and how (often) the rules fire. Our empirical evaluation shows that we can answer a wide range of probabilistic queries on relational data while being robust to missing, out-of-domain data and partial counts. We show that our method generalizes to different distributions outperforming strong baselines. Moreover, due to the clear probabilistic semantics of MSPNs we have informative model interpretations.