document: The mathematics of causal inference 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 .
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