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                                         Generalizability of
                                    Causal and Statistical Relations


                                                  Elias Bareinboim
                                            Cognitive Systems Laboratory
                                            Computer Science Department
                                         University of California, Los Angeles
                                                    eb@cs.ucla.edu

                                                       Abstract

   The problem of generalizability of empirical findings (experimental and observational) to new environments,
   settings, and populations is one of the central problems in causal inference. Experiments in the sciences are
   invariably conducted with the intent of being used elsewhere (e.g., outside the laboratory), where conditions are
   likely to be different. This practice is based on the premise that, due to certain commonalities between the source
   and target environments, causal claims would be valid even where experiments have never been performed.
   Despite the extensive amount of empirical work relying on this premise, practically no formal treatments have
   been able to determine the conditions under which generalizations are valid, in some formal sense.
   Our work develops a theoretical framework for understanding, representing, and algorithmizing the general-
   ization problem as encountered in many practical settings in data-intensive fields. Our framework puts many
   apparently disparate generalization problems under the same theoretical umbrella. In this talk, I will start with a
   brief review of the basic concepts, principles, and mathematical tools necessary for reasoning about causal and
   counterfactual relations [1, 2, 3]. I will then introduce two special problems under the generalization umbrella.
   First, I will discuss “transportability” [4, 5, 6], that is, how information acquired by experiments in one setting
   can be reused to answer queries in another, possibly different setting where only limited information can be
   collected. This question embraces several sub-problems treated informally in the literature under rubrics such as
   “external validity” [7, 8], “meta-analysis” [9], “heterogeneity” [10], “quasi-experiments” [11, Ch. 3]. Further, I
   will discuss selection bias [12, 13, 14], that is, how knowledge from a sampled subpopulation can be generalized
   to the entire population when sampling selection is not random, but determined by variables in the analysis,
   which means units are preferentially excluded from the sample.
   In both problems, we provide complete conditions and algorithms to support the inductive step required in
   the corresponding task. This characterization distinguishes between estimable and non-estimable queries, and
   identifies which pieces of scientific knowledge need to be collected in each study to construct a bias-free estimate
   of the target query. The problems discussed in this work have applications in several empirical sciences such as
   Bioinformatics, Medicine, Economics, Social Sciences as well as in data-driven fields such as Machine Learning,
   Artificial Intelligence and Statistics.


References

[1] J. Pearl. The deductive approach to causal inference. Journal of Causal Inference, 2(2):115–130, 2014.

[2] P. Spirtes, C.N. Glymour, and R. Scheines. Causation, Prediction, and Search. Springer-Verlag, New York, 1993.

[3] E. Bareinboim, C. Brito, and J. Pearl. Local characterizations of causal bayesian networks. Lecture Notes in Artificial
    Intelligence, 7205:1–17, 2012.

[4] J. Pearl and E. Bareinboim. External validity: From do-calculus to transportability across populations. Statistical
    Science, forthcoming, 2014.
 [5] E. Bareinboim and J. Pearl. Causal transportability with limited experiments. In Proceedings of the Twenty-Seventh
     National Conference on Artificial Intelligence, pages 95–101, Menlo Park, CA, 2013. AAAI Press.
 [6] E. Bareinboim and J. Pearl. A general algorithm for deciding transportability of experimental results. Journal of
     Causal Inference, 1(1):107–134, 2013.

 [7] D. Campbell and J. Stanley. Experimental and Quasi-Experimental Designs for Research. Wadsworth Publishing,
     Chicago, 1963.
 [8] C. Manski. Identification for Prediction and Decision. Harvard University Press, Cambridge, Massachusetts, 2007.
 [9] Gene V. Glass. Primary, secondary, and meta-analysis of research. Educational Researcher, 5(10):pp. 3–8, 1976.

[10] M. Höfler, A.T. Gloster, and J. Hoyer. Causal effects in psychotherapy: Counterfactuals counteract overgeneraliza-
     tion. Psychotherapy Research, 2010.
[11] W.R. Shadish, T.D. Cook, and D.T. Campbell. Experimental and Quasi-Experimental Designs for Generalized Causal
     Inference. Houghton-Mifflin, Boston, second edition, 2002.
[12] V. Didelez, S. Kreiner, and N. Keiding. Graphical models for inference under outcome-dependent sampling. Statisti-
     cal Science, 25(3):368–387, 2010.
[13] E. Bareinboim and J. Pearl. Controlling selection bias in causal inference. In Proceedings of the 15th International
     Conference on Artificial Intelligence and Statistics (AISTATS), pages 100–108. JMLR, April 21-23 2012.
[14] E. Bareinboim, J. Tian, and J. Pearl. Recovering from selection bias in causal and statistical inference. In Proceedings
     of the Twenty-Eight National Conference on Artificial Intelligence (AAAI 2014), Menlo Park, CA, 2014. AAAI Press.

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