We consider the problem of explaining a tractable deep probabilistic model, the Sum-Product Networks (SPNs).To this effect, we define the notion of a context-specific independence tree and present an iterative algorithm that converts an SPN to a CSI-tree. The resulting CSI-tree is both interpretable and explainable to the domain expert. To further compress the tree, we approximate the CSIs by fitting a supervised classifier. Our extensive empirical evaluations on synthetic, standard, and real-world clinical data sets demonstrate that the resulting models exhibit superior explainability without loss in performance.
While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed around personal health. Our empirical evaluation on three benchmark data sets as well as a synthetic health data set clearly demonstrates that interventional SPNs indeed are both expressive in modelling and flexible in adapting to the interventions.