Title: The Potential Outcomes Calculus
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. 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.
Dr. Shpitser is a John C. Malone Assistant Professor at the department of Computer Science at Johns Hopkins University. His areas of interest include causal and probabilistic inference in graphical models, algorithmic fairness, and inference in the presence of missing or dependent data. His primary applications are in public health and medicine.