Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias

Patrick Forré, Joris M. Mooij
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:71-80, 2020.

Abstract

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also generalize adjustment criteria and formulas from the acyclic setting to the general one (i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal effects from observational data that was (partially) gathered under selection bias and cycles. This generalizes the backdoor criterion, the selection-backdoor criterion and extensions of these to arbitrary ioSCMs. Together, our results thus enable causal reasoning in the presence of cycles, latent confounders and selection bias. Finally, we extend the ID algorithm for the identification of causal effects to ioSCMs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-forre20a, title = {Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias}, author = {Forr{\'{e}}, Patrick and Mooij, Joris M.}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {71--80}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/forre20a/forre20a.pdf}, url = {https://proceedings.mlr.press/v115/forre20a.html}, abstract = {We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also generalize adjustment criteria and formulas from the acyclic setting to the general one (i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal effects from observational data that was (partially) gathered under selection bias and cycles. This generalizes the backdoor criterion, the selection-backdoor criterion and extensions of these to arbitrary ioSCMs. Together, our results thus enable causal reasoning in the presence of cycles, latent confounders and selection bias. Finally, we extend the ID algorithm for the identification of causal effects to ioSCMs.} }
Endnote
%0 Conference Paper %T Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias %A Patrick Forré %A Joris M. Mooij %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-forre20a %I PMLR %P 71--80 %U https://proceedings.mlr.press/v115/forre20a.html %V 115 %X We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also generalize adjustment criteria and formulas from the acyclic setting to the general one (i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal effects from observational data that was (partially) gathered under selection bias and cycles. This generalizes the backdoor criterion, the selection-backdoor criterion and extensions of these to arbitrary ioSCMs. Together, our results thus enable causal reasoning in the presence of cycles, latent confounders and selection bias. Finally, we extend the ID algorithm for the identification of causal effects to ioSCMs.
APA
Forré, P. & Mooij, J.M.. (2020). Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:71-80 Available from https://proceedings.mlr.press/v115/forre20a.html.

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