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arXiv · 2408.07545

$\chi$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
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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.

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Harsh Poonia, Moritz Willig, Zhongjie Yu, Matej Zečević, Kristian Kersting, Devendra Singh Dhami. 2024-08-14. $\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains. https://arxiv.org/abs/2408.07545

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