A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects

Daniel Malinsky, Ilya Shpitser, Thomas Richardson
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:3080-3088, 2019.

Abstract

The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator. Such problems include analyses of path-specific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (po-calculus), a natural generalization of do-calculus for arbitrary potential outcomes. We thereby provide a bridge between identification approaches which have their origins in artificial intelligence and statistics, respectively. We use po-calculus to give a complete identification algorithm for conditional path-specific effects with applications to problems in mediation analysis and algorithmic fairness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-malinsky19b, title = {A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects}, author = {Malinsky, Daniel and Shpitser, Ilya and Richardson, Thomas}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {3080--3088}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/malinsky19b/malinsky19b.pdf}, url = {https://proceedings.mlr.press/v89/malinsky19b.html}, abstract = {The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator. Such problems include analyses of path-specific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (po-calculus), a natural generalization of do-calculus for arbitrary potential outcomes. We thereby provide a bridge between identification approaches which have their origins in artificial intelligence and statistics, respectively. We use po-calculus to give a complete identification algorithm for conditional path-specific effects with applications to problems in mediation analysis and algorithmic fairness.} }
Endnote
%0 Conference Paper %T A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects %A Daniel Malinsky %A Ilya Shpitser %A Thomas Richardson %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-malinsky19b %I PMLR %P 3080--3088 %U https://proceedings.mlr.press/v89/malinsky19b.html %V 89 %X The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator. Such problems include analyses of path-specific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (po-calculus), a natural generalization of do-calculus for arbitrary potential outcomes. We thereby provide a bridge between identification approaches which have their origins in artificial intelligence and statistics, respectively. We use po-calculus to give a complete identification algorithm for conditional path-specific effects with applications to problems in mediation analysis and algorithmic fairness.
APA
Malinsky, D., Shpitser, I. & Richardson, T.. (2019). A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:3080-3088 Available from https://proceedings.mlr.press/v89/malinsky19b.html.

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