Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders

Patrick Forré, Joris M. Mooij
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:268-277, 2018.

Abstract

We address the problem of causal discovery from data, making use of the recently pro- posed causal modeling framework of modu- lar structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce $\sigma$-connection graphs ($\sigma$-CG), a new class of mixed graphs (containing undi- rected, bidirected and directed edges) with ad- ditional structure, and extend the concept of $\sigma$-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to $\sigma$-CGs. We prove the closedness of $\sigma$-separation under marginalisa- tion and conditioning and exploit this to im- plement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algo- rithm that can handle non-linear functional re- lations, latent confounders, cyclic causal rela- tionships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algo- rithm recovers features of the causal graph of modular structural causal models.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-forre18a, title = {Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders}, author = {Forr{\'e}, Patrick and Mooij, Joris M.}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {268--277}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/forre18a/forre18a.pdf}, url = {https://proceedings.mlr.press/r16/forre18a.html}, abstract = {We address the problem of causal discovery from data, making use of the recently pro- posed causal modeling framework of modu- lar structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce $\sigma$-connection graphs ($\sigma$-CG), a new class of mixed graphs (containing undi- rected, bidirected and directed edges) with ad- ditional structure, and extend the concept of $\sigma$-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to $\sigma$-CGs. We prove the closedness of $\sigma$-separation under marginalisa- tion and conditioning and exploit this to im- plement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algo- rithm that can handle non-linear functional re- lations, latent confounders, cyclic causal rela- tionships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algo- rithm recovers features of the causal graph of modular structural causal models.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders %A Patrick Forré %A Joris M. Mooij %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-forre18a %I PMLR %P 268--277 %U https://proceedings.mlr.press/r16/forre18a.html %V R16 %X We address the problem of causal discovery from data, making use of the recently pro- posed causal modeling framework of modu- lar structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce $\sigma$-connection graphs ($\sigma$-CG), a new class of mixed graphs (containing undi- rected, bidirected and directed edges) with ad- ditional structure, and extend the concept of $\sigma$-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to $\sigma$-CGs. We prove the closedness of $\sigma$-separation under marginalisa- tion and conditioning and exploit this to im- plement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algo- rithm that can handle non-linear functional re- lations, latent confounders, cyclic causal rela- tionships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algo- rithm recovers features of the causal graph of modular structural causal models. %Z Reissued by PMLR on 04 October 2026.
APA
Forré, P. & Mooij, J.M.. (2018). Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:268-277 Available from https://proceedings.mlr.press/r16/forre18a.html. Reissued by PMLR on 04 October 2026.

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