Causality via potential outcomes

Relationship to Pearl-style do-calculus
Heterogeneous treatment effects
Instrumental variables
External validity
Use in ML
Propensity matching
Causal forests
Double learning
References

A sister(?) field of the DAG-centric causal inference. I say sister field because the patriarch of the DAG school, Judea Pearl, seems to regard potential outcomes as a special case of causal DAG reasoning, claiming a proud lineage going back to Seward Wright. OTOH, proponents of potential outcomes, especially Rubin, seem to regard it as the actually-practical way to do causal reasoning and claim a proud lineage going to Jerzy Neyman. In practice I suspect we as users do not need to worry excessively about the border disputes.

Rubin and Waterman (2006) comes recommended by Shalizi as:

A good description of Rubin et al.’s methods for causal inference, adapted to the meanest understanding. […] Rubin and Waterman do a very good job of explaining, in a clear and concrete problem, just how and why the newer techniques of causal inference are valuable, with just enough technical detail that it doesn’t seem like magic.

Relationship to Pearl-style do-calculus

Uri Shalit argues

Rubin and Pearl are kind of “academic enemies”. Though neither completely dismisses the other, they both make snide remarks about the other’s work. Pearl shows in his book exactly how Neyman-Rubin potential outcomes can be derived from causal graphs. As far as I know Rubin never really makes an attempt to address Pearl’s ideas directly. However, Rubin, being a statistician, made significant contributions to the practice of real-world causal inference, which go beyond Pearl’s interests. Jamie Robins also made seminal contributions to this subject. You can read some of the debate on Andrew Gelman’s blog here. Pearl writes in the comment section and in that blog post there are links to follow up posts.

I am more familiar with the Pearl-style approach. The two connect by, e.g. Single World Intervention Graphs (Richardson and Robins 2013).

Heterogeneous treatment effects

See interaction effects for now.

Instrumental variables

see instrumental variables.

External validity

Dataset shift etc. See external validity.

Use in ML

See causality in ML.

Propensity matching

TODO

Causal forests

To follow up: proximity matrix in causal random forest.

The GRF Algorithm. Haaya Naushan: Causal Machine Learning for Econometrics: Causal Forests.

Double learning

See causality and ML.

References

Athey, Susan, and Stefan Wager. 2019. “Estimating Treatment Effects with Causal Forests: An Application.” arXiv:1902.07409 [Stat], February.

Bareinboim, Elias, and Judea Pearl. 2016. “Causal Inference and the Data-Fusion Problem.” Proceedings of the National Academy of Sciences 113 (27): 7345–52.

Bloniarz, Adam, Hanzhong Liu, Cun-Hui Zhang, Jasjeet Sekhon, and Bin Yu. 2015. “Lasso Adjustments of Treatment Effect Estimates in Randomized Experiments.” arXiv:1507.03652 [Math, Stat], July.

Brodersen, Kay H., Fabian Gallusser, Jim Koehler, Nicolas Remy, and Steven L. Scott. 2015. “Inferring Causal Impact Using Bayesian Structural Time-Series Models.” The Annals of Applied Statistics 9 (1): 247–74.

Bühlmann, Peter. 2020. “Invariance, Causality and Robustness.” Statistical Science 35 (3): 404–26.

Chau, Siu Lun, Jean-François Ton, Javier González, Yee Whye Teh, and Dino Sejdinovic. 2021. “BayesIMP: Uncertainty Quantification for Causal Data Fusion,” June.

Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. 2016. “Double/Debiased Machine Learning for Treatment and Causal Parameters.” arXiv:1608.00060 [Econ, Stat], July.

Chernozhukov, Victor, Christian Hansen, and Martin Spindler. 2015. “Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach.” Annual Review of Economics 7 (1): 649–88.

Dahlhaus, Rainer, and Michael Eichler. 2003. “Causality and Graphical Models in Time Series Analysis.” Oxford Statistical Science Series, 115–37.

Dawid, Philip. 2021. “Decision-Theoretic Foundations for Statistical Causality.” Journal of Causal Inference 9 (1): 39–77.

De Luna, Xavier, Ingeborg Waernbaum, and Thomas S. Richardson. 2011. “Covariate Selection for the Nonparametric Estimation of an Average Treatment Effect.” Biometrika, October, asr041.

Gelman, Andrew. 2010. “Causality and Statistical Learning.” American Journal of Sociology 117 (3): 955–66.

Gelman, Andrew, and Xiao-Li Meng. 2004. Applied Bayesian Modeling and Causal Inference From Incomplete-Data Perspectives. John Wiley & Sons.

Gelman, Andrew, and Cosma Rohilla Shalizi. 2013. “Philosophy and the Practice of Bayesian Statistics.” British Journal of Mathematical and Statistical Psychology 66 (1): 8–38.

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Imbens, Guido, and Konrad Menzel. 2021. “A Causal Bootstrap.” The Annals of Statistics 49 (3): 1460–88.

Kennedy, Edward H., Jacqueline A. Mauro, Michael J. Daniels, Natalie Burns, and Dylan S. Small. 2019. “Handling Missing Data in Instrumental Variable Methods for Causal Inference.” Annual Review of Statistics and Its Application 6 (1): 125–48.

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Malinsky, Daniel, Ilya Shpitser, and Thomas Richardson. 2019. “A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects.” arXiv:1903.03662 [Stat], March.

Manski, Charles F. 2011. “Choosing Treatment Policies Under Ambiguity.” Annual Review of Economics 3 (1): 25–49.

Meinshausen, Nicolai. 2018. “Causality from a Distributional Robustness Point of View.” In 2018 IEEE Data Science Workshop (DSW), 6–10.

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Pearl, Judea. 2009. “Causal Inference in Statistics: An Overview.” Statistics Surveys 3: 96–146.

Pearl, Judea, and Elias Bareinboim. 2014. “External Validity: From Do-Calculus to Transportability Across Populations.” Statistical Science 29 (4): 579–95.

Richardson, Thomas S., and James M. Robins. 2013. “Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality.” Citeseer.

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