$\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains
<|reference_start|>$\chi$SPN: 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 ($\chi$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.<|reference_end|>
@article{poonia2024$\chi$spn:,
    title={$\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal
  Inference in Hybrid Domains},
    author={Harsh Poonia, Moritz Willig, Zhongjie Yu, Matej Zev{c}evi'c,
  Kristian Kersting, Devendra Singh Dhami},
    journal={arXiv preprint arXiv:2408.07545},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07545},
    primaryClass={cs.LG cs.AI}
}