Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles

Joris M. Mooij, Tom Claassen
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1159-1168, 2020.

Abstract

While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that—surprisingly—the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and sigma-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-m-mooij20a, title = {Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles}, author = {M. Mooij, Joris and Claassen, Tom}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1159--1168}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/m-mooij20a/m-mooij20a.pdf}, url = {https://proceedings.mlr.press/v124/m-mooij20a.html}, abstract = {While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that—surprisingly—the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and sigma-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).} }
Endnote
%0 Conference Paper %T Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles %A Joris M. Mooij %A Tom Claassen %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-m-mooij20a %I PMLR %P 1159--1168 %U https://proceedings.mlr.press/v124/m-mooij20a.html %V 124 %X While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that—surprisingly—the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and sigma-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).
APA
M. Mooij, J. & Claassen, T.. (2020). Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1159-1168 Available from https://proceedings.mlr.press/v124/m-mooij20a.html.

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