A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects
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.
Keywords
Cite
@article{arxiv.1903.03662,
title = {A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects},
author = {Daniel Malinsky and Ilya Shpitser and Thomas Richardson},
journal= {arXiv preprint arXiv:1903.03662},
year = {2019}
}