χSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains

Causal inference in hybrid domains, characterized by a mixture of discrete and continuous variables, presents a formidable challenge. We take a step towards this direction and propose Characteristic Interventional Sum-Product Network (χSPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. χSPN uses characteristic functions in the leaves of an interventional SPN (iSPN) thereby providing a unified view for discrete and continuous random variables through the Fourier-Stieltjes transform of the probability measures. A neural network is used to estimate the parameters of the learned iSPN using the intervened data. Our experiments on 3 synthetic heterogeneous datasets suggest that χSPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that χSPN generalize to multiple interventions while being trained only on a single intervention data.