The mathematics of causal inference

Abstract

I will review concepts, principles, and mathematical tools that were found useful in applications involving causal and counterfactual relationships. This semantical framework, enriched with a few ideas from logic and graph theory, gives rise to a complete, coherent, and friendly calculus of causation that unifies the graphical and counterfactual approaches to causation and resolves many long-standing problems in several of the sciences. These include questions of causal effect estimation, policy analysis, and the integration of data from diverse studies. Of special interest to KDD researchers would be the following topics: The Mediation Formula, and what it tells us about direct and indirect effects. What mathematics can tell us about "external validity" or "generalizing from experiments" What can graph theory tell us about recovering from sample-selection bias.