Identifying Partially Observed Causal Models from Heterogeneous/Nonstationary Data

Xinshuai Dong, Haoyue Dai, Ignavier Ng, Peter Spirtes, Kun Zhang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:25763-25787, 2026.

Abstract

Estimating causal structure in the presence of latent variables is an important yet challenging problem. Recent works have shown that distributional constraints, such as rank deficiency constraints of the covariance matrices, can be exploited to recover the underlying causal structure involving latent variables. However, real-world data often exhibit heterogeneity/nonstationarity, which pose challenges to existing methods. In this work, we develop a principled approach for identifying the structure of partially observed linear causal models from heterogenous/nonstationary data. We first formulate a class of heterogenous/nonstationary, partially observed linear causal models and prove that their distributional constraints are equivalent to those in the homogeneous case. Building on this, we propose a novel rank deficiency test that can efficiently handle heterogenous/nonstationary data, and further establish identifiability results for recovering the causal structure involving latent variables. We also provide a method to identify which variables exhibit distribution shifts, i.e., whose causal mechanisms vary across domains. Experiments on simulated and real-world data validate our theoretical findings and the effectiveness of our method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-dong26a, title = {Identifying Partially Observed Causal Models from {H}eterogeneous/{N}onstationary Data}, author = {Dong, Xinshuai and Dai, Haoyue and Ng, Ignavier and Spirtes, Peter and Zhang, Kun}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {25763--25787}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/dong26a/dong26a.pdf}, url = {https://proceedings.mlr.press/v306/dong26a.html}, abstract = {Estimating causal structure in the presence of latent variables is an important yet challenging problem. Recent works have shown that distributional constraints, such as rank deficiency constraints of the covariance matrices, can be exploited to recover the underlying causal structure involving latent variables. However, real-world data often exhibit heterogeneity/nonstationarity, which pose challenges to existing methods. In this work, we develop a principled approach for identifying the structure of partially observed linear causal models from heterogenous/nonstationary data. We first formulate a class of heterogenous/nonstationary, partially observed linear causal models and prove that their distributional constraints are equivalent to those in the homogeneous case. Building on this, we propose a novel rank deficiency test that can efficiently handle heterogenous/nonstationary data, and further establish identifiability results for recovering the causal structure involving latent variables. We also provide a method to identify which variables exhibit distribution shifts, i.e., whose causal mechanisms vary across domains. Experiments on simulated and real-world data validate our theoretical findings and the effectiveness of our method.} }
Endnote
%0 Conference Paper %T Identifying Partially Observed Causal Models from Heterogeneous/Nonstationary Data %A Xinshuai Dong %A Haoyue Dai %A Ignavier Ng %A Peter Spirtes %A Kun Zhang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-dong26a %I PMLR %P 25763--25787 %U https://proceedings.mlr.press/v306/dong26a.html %V 306 %X Estimating causal structure in the presence of latent variables is an important yet challenging problem. Recent works have shown that distributional constraints, such as rank deficiency constraints of the covariance matrices, can be exploited to recover the underlying causal structure involving latent variables. However, real-world data often exhibit heterogeneity/nonstationarity, which pose challenges to existing methods. In this work, we develop a principled approach for identifying the structure of partially observed linear causal models from heterogenous/nonstationary data. We first formulate a class of heterogenous/nonstationary, partially observed linear causal models and prove that their distributional constraints are equivalent to those in the homogeneous case. Building on this, we propose a novel rank deficiency test that can efficiently handle heterogenous/nonstationary data, and further establish identifiability results for recovering the causal structure involving latent variables. We also provide a method to identify which variables exhibit distribution shifts, i.e., whose causal mechanisms vary across domains. Experiments on simulated and real-world data validate our theoretical findings and the effectiveness of our method.
APA
Dong, X., Dai, H., Ng, I., Spirtes, P. & Zhang, K.. (2026). Identifying Partially Observed Causal Models from Heterogeneous/Nonstationary Data. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:25763-25787 Available from https://proceedings.mlr.press/v306/dong26a.html.

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