$χ$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains
This addresses a challenging problem in causal inference for domains with mixed variable types, but it is incremental as it builds on existing interventional SPN frameworks.
The paper tackles causal inference in hybrid domains with mixed discrete and continuous variables by proposing $\chi$SPN, a method that estimates interventional distributions using characteristic functions and neural networks. Experiments on 3 synthetic datasets show it effectively captures interventional distributions and generalizes to multiple interventions with single-intervention training.
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 ($χ$SPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. $χ$SPN 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 $χ$SPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that $χ$SPN generalize to multiple interventions while being trained only on a single intervention data.