Causal Discovery in Mixtures of Populations

Bijan Mazaheri, Spencer L. Gordon, Yuval Rabani, Leonard Schulman
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:4457-4478, 2026.

Abstract

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a “source” which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying {DAG}. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-mazaheri26c, title = {Causal Discovery in Mixtures of Populations}, author = {Mazaheri, Bijan and Gordon, Spencer L. and Rabani, Yuval and Schulman, Leonard}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {4457--4478}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/mazaheri26c/mazaheri26c.pdf}, url = {https://proceedings.mlr.press/v337/mazaheri26c.html}, abstract = {Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a “source” which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying {DAG}. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.} }
Endnote
%0 Conference Paper %T Causal Discovery in Mixtures of Populations %A Bijan Mazaheri %A Spencer L. Gordon %A Yuval Rabani %A Leonard Schulman %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-mazaheri26c %I PMLR %P 4457--4478 %U https://proceedings.mlr.press/v337/mazaheri26c.html %V 337 %X Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a “source” which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying {DAG}. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.
APA
Mazaheri, B., Gordon, S.L., Rabani, Y. & Schulman, L.. (2026). Causal Discovery in Mixtures of Populations. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:4457-4478 Available from https://proceedings.mlr.press/v337/mazaheri26c.html.

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