Models based on potential outcomes, also known as counterfactuals, were introduced by Neyman (1923) and later popularized by Rubin (1974). Such models are used extensively within biostatistics, statistics, political science, economics, and epidemiology for reasoning about causation. Directed acyclic graphs (DAGs), introduced by Wright (1921), are another formalism used to represent causal systems. Graphs are also extensively used in computer science, bioinformatics, sociology and epidemiology.

This talk will present a simple approach to unifying these two approaches via a new graph, termed the Single-World Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on a set of treatment variables. The nodes on the SWIG are the corresponding counterfactual random variables. The SWIG is derived from a causal DAG via a simple node-splitting transformation. The theory will be illustrated with a number of examples. Finally, it will be shown that SWIGs avoid a number of pitfalls that are present in an alternative approach to unification, based on “twin networks,” that has been advocated by Pearl (2000).

This is joint work with James Robins (Harvard School of Public Health).

Link to paper:


Thomas S. Richardson is a Professor of Statistics at the University of Washington. He is also the Director of the Center for Statistics and the Social Sciences at the University of Washington. His research interests include machine learning, multivariate statistics, graphical models, and causal inference. Most recently he has developed parametrizations and fitting algorithms for graphical models with both directed (→) and bi-directed edges (↔); these models are designed to represent causal systems in which unmeasured “confounding” variables may be present. Professor Richardson is a Fellow of the Center for Advanced Studies in the Behavioral Sciences at Stanford University. He was also a Visiting Senior Research Fellow at Jesus College, Oxford, in 2008. He received the Best Paper Award at the Conference for Uncertainty in Artificial Intelligence (UAI) in 2009.