$\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains

Harsh Poonia, Moritz Willig, Zhongjie Yu, Matej Zečević, Kristian Kersting, Devendra Singh Dhami

Keywords: causality, hybrid domains, sum-product networks, characteristic functions

TL;DR: We present the 1st causal based based on characteristic functions and sum-product networks for hybrid domains.

Abstract: 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 \textbf{Ch}aracteristic \textbf{I}nterventional Sum-Product Network ($\chi$SPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. $\chi$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 $\chi$SPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that $\chi$SPN generalize to multiple interventions while being trained only on a single intervention data.

Submission Number: 14