Causal Identification under Markov Equivalence: Completeness Results

Amin Jaber, Jiji Zhang, Elias Bareinboim
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2981-2989, 2019.

Abstract

Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-jaber19a, title = {Causal Identification under {M}arkov Equivalence: Completeness Results}, author = {Jaber, Amin and Zhang, Jiji and Bareinboim, Elias}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {2981--2989}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/jaber19a/jaber19a.pdf}, url = {https://proceedings.mlr.press/v97/jaber19a.html}, abstract = {Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.} }
Endnote
%0 Conference Paper %T Causal Identification under Markov Equivalence: Completeness Results %A Amin Jaber %A Jiji Zhang %A Elias Bareinboim %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-jaber19a %I PMLR %P 2981--2989 %U https://proceedings.mlr.press/v97/jaber19a.html %V 97 %X Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.
APA
Jaber, A., Zhang, J. & Bareinboim, E.. (2019). Causal Identification under Markov Equivalence: Completeness Results. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:2981-2989 Available from https://proceedings.mlr.press/v97/jaber19a.html.

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