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

Harsh Poonia, Moritz Willig, Zhongjie Yu, Matej Ze\vcević, Kristian Kersting, Devendra Singh Dhami
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:3004-3020, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-poonia24a, title = {$χ$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains}, author = {Poonia, Harsh and Willig, Moritz and Yu, Zhongjie and Ze\v{}cevi\'c, Matej and Kersting, Kristian and Dhami, Devendra Singh}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {3004--3020}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/poonia24a/poonia24a.pdf}, url = {https://proceedings.mlr.press/v244/poonia24a.html}, 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.} }
Endnote
%0 Conference Paper %T $χ$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains %A Harsh Poonia %A Moritz Willig %A Zhongjie Yu %A Matej Ze\vcević %A Kristian Kersting %A Devendra Singh Dhami %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-poonia24a %I PMLR %P 3004--3020 %U https://proceedings.mlr.press/v244/poonia24a.html %V 244 %X 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.
APA
Poonia, H., Willig, M., Yu, Z., Ze\vcević, M., Kersting, K. & Dhami, D.S.. (2024). $χ$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:3004-3020 Available from https://proceedings.mlr.press/v244/poonia24a.html.

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