  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.
