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

TL;DR

This paper introduces $ ext{ extchi}$SPN, a novel model for causal inference in hybrid domains with mixed discrete and continuous variables, using characteristic functions to estimate interventional distributions effectively.

Contribution

The paper proposes $ ext{ extchi}$SPN, a new interventional sum-product network leveraging characteristic functions for unified causal inference in hybrid domains with mixed variable types.

Findings

$ ext{ extchi}$SPN accurately captures interventional distributions in synthetic datasets.

It generalizes to multiple interventions from single intervention training.

The model is expressive and causally adequate 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 Characteristic Interventional 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.