Explaining Deep Tractable Probabilistic Models: The sum-product network case

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.

Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models

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.