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 proposed causal modeling framework of modular 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 undirected, bidirected and directed edges) with additional 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 marginalisation and conditioning and exploit this to implement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algorithm that can handle non-linear functional relations, latent confounders, cyclic causal relationships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algorithm 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 proposed causal modeling framework of modular 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 undirected, bidirected and directed edges) with additional 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 marginalisation and conditioning and exploit this to implement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algorithm that can handle non-linear functional relations, latent confounders, cyclic causal relationships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algorithm 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 proposed causal modeling framework of modular 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 undirected, bidirected and directed edges) with additional 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 marginalisation and conditioning and exploit this to implement a test of $\sigma$-separation on a $\sigma$-CG. This then leads us to the first causal discovery algorithm that can handle non-linear functional relations, latent confounders, cyclic causal relationships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algorithm 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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