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Title: A potential outcomes calculus for identifying conditional path-specific effects Authors:  Daniel Malinsky - Columbia University (United States) [presenting]
Ilya Shpitser - Johns Hopkins University (United States)
Thomas Richardson - University of Washington (United States)
Abstract: The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions. It has been proven complete for several 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. 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.