A Potential Outcomes Calculus for Identifying Conditional PathSpecific Effects
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Proceedings of Machine Learning Research, PMLR 89:30803088, 2019.
Abstract
The docalculus is a wellknown 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 docalculus 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 pathspecific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (pocalculus), a natural generalization of docalculus for arbitrary potential outcomes. We thereby provide a bridge between identification approaches which have their origins in artificial intelligence and statistics, respectively. We use pocalculus to give a complete identification algorithm for conditional pathspecific effects with applications to problems in mediation analysis and algorithmic fairness.
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