Causality via potential outcomes

Neyman-Rubin, counterfactuals, potential outcomes, instrumental variables and related tricks



A sister(?) field of the DAG-centric causal inference.

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.

Counterfactuals

🏗

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.

Instrumental variables

External validity

Dataset shift etc. See external validity.

Causal time series

As with other time series methods, has its own issues.

🏗 find out how Causal impact works. (Based on Brodersen et al. (2015).)

The CausalImpact R package implements an approach to estimating the causal effect of a designed intervention on a time series. For example, how many additional daily clicks were generated by an advertising campaign? Answering a question like this can be difficult when a randomized experiment is not available. The package aims to address this difficulty using a structural Bayesian time-series model to estimate how the response metric might have evolved after the intervention if the intervention had not occurred.

More generally, we might be concerned with continuous time.

References

Bareinboim, Elias, and Judea Pearl. 2016. “Causal Inference and the Data-Fusion Problem.” Proceedings of the National Academy of Sciences 113 (27): 7345–52. https://doi.org/10.1073/pnas.1510507113.
Bloniarz, Adam, Hanzhong Liu, Cun-Hui Zhang, Jasjeet Sekhon, and Bin Yu. 2015. “Lasso Adjustments of Treatment Effect Estimates in Randomized Experiments.” July 13, 2015. http://arxiv.org/abs/1507.03652.
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. https://doi.org/10.1214/14-AOAS788.
Bühlmann, Peter. 2020. “Invariance, Causality and Robustness.” Statistical Science 35 (3): 404–26. https://doi.org/10.1214/19-STS721.
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.” July 29, 2016. http://arxiv.org/abs/1608.00060.
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. https://doi.org/10.1146/annurev-economics-012315-015826.
Dahlhaus, Rainer, and Michael Eichler. 2003. “Causality and Graphical Models in Time Series Analysis.” Oxford Statistical Science Series, 115–37. http://galton.uchicago.edu/ eichler/hsss.pdf.
De Luna, Xavier, Ingeborg Waernbaum, and Thomas S. Richardson. 2011. “Covariate Selection for the Nonparametric Estimation of an Average Treatment Effect.” Biometrika, October, asr041. https://doi.org/10.1093/biomet/asr041.
Gelman, Andrew. 2010. “Causality and Statistical Learning.” American Journal of Sociology 117 (3): 955–66. https://doi.org/10.1086/662659.
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. https://doi.org/10.1111/j.2044-8317.2011.02037.x.
Greenland, Sander, and James M Robins. 2009. “Identifiability, Exchangeability and Confounding Revisited.” Epidemiologic Perspectives & Innovations : EP+I 6 (September): 4. https://doi.org/10.1186/1742-5573-6-4.
Heinze-Deml, Christina, Marloes H. Maathuis, and Nicolai Meinshausen. 2018. “Causal Structure Learning.” Annual Review of Statistics and Its Application 5 (1): 371–91. https://doi.org/10.1146/annurev-statistics-031017-100630.
Imbens, Guido W. 2014. “Instrumental Variables: An Econometrician’s Perspective.” Statistical Science 29 (3): 323–58. https://doi.org/10.1214/14-STS480.
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. https://doi.org/10.1146/annurev-statistics-031017-100353.
Kohler, Ulrich, Frauke Kreuter, and Elizabeth A. Stuart. 2019. “Nonprobability Sampling and Causal Analysis.” Annual Review of Statistics and Its Application 6 (1): 149–72. https://doi.org/10.1146/annurev-statistics-030718-104951.
Kuang, Zhaobin, Frederic Sala, Nimit Sohoni, Sen Wu, Aldo Córdova-Palomera, Jared Dunnmon, James Priest, and Christopher Re. 2020. “Ivy: Instrumental Variable Synthesis for Causal Inference.” In International Conference on Artificial Intelligence and Statistics, 398–410. PMLR. http://proceedings.mlr.press/v108/kuang20a.html.
Künzel, Sören R., Jasjeet S. Sekhon, Peter J. Bickel, and Bin Yu. 2019. “Metalearners for Estimating Heterogeneous Treatment Effects Using Machine Learning.” Proceedings of the National Academy of Sciences 116 (10): 4156–65. https://doi.org/10.1073/pnas.1804597116.
Lattimore, Finnian Rachel. 2017. “Learning How to Act: Making Good Decisions with Machine Learning.” https://doi.org/10.25911/5d67b766194ec.
Malinsky, Daniel, Ilya Shpitser, and Thomas Richardson. 2019. “A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects.” March 8, 2019. http://arxiv.org/abs/1903.03662.
Meinshausen, Nicolai. 2018. “Causality from a Distributional Robustness Point of View.” In 2018 IEEE Data Science Workshop (DSW), 6–10. https://doi.org/10.1109/DSW.2018.8439889.
Morgan, Stephen L., and Christopher Winship. 2015. Counterfactuals and Causal Inference. Cambridge University Press.
Pearl, Judea. 2009. “Causal Inference in Statistics: An Overview.” Statistics Surveys 3: 96–146. https://doi.org/10.1214/09-SS057.
Pearl, Judea, and Elias Bareinboim. 2014. “External Validity: From Do-Calculus to Transportability Across Populations.” Statistical Science 29 (4): 579–95. https://doi.org/10.1214/14-STS486.
Rothenhäusler, Dominik, Nicolai Meinshausen, Peter Bühlmann, and Jonas Peters. 2020. “Anchor Regression: Heterogeneous Data Meets Causality.” May 8, 2020. http://arxiv.org/abs/1801.06229.
Rubin, Donald B, and Richard P Waterman. 2006. “Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology.” Statistical Science 21 (2): 206–22. https://doi.org/10.1214/088342306000000259.
Schulam, Peter, and Suchi Saria. 2017. “Reliable Decision Support Using Counterfactual Models.” In Proceedings of the 31st International Conference on Neural Information Processing Systems, 1696–706. NIPS’17. Red Hook, NY, USA: Curran Associates Inc. http://papers.nips.cc/paper/6767-reliable-decision-support-using-counterfactual-models.pdf.
Shalizi, Cosma Rohilla. n.d. “Advanced Data Analysis from an Elementary Point of View,” 848.
Sharma, Amit, Jake M. Hofman, and Duncan J. Watts. 2015. “Estimating the Causal Impact of Recommendation Systems from Observational Data.” Proceedings of the Sixteenth ACM Conference on Economics and Computation - EC ’15, 453–70. https://doi.org/10.1145/2764468.2764488.
Shpitser, Ilya, Karthika Mohan, and Judea Pearl. 2015. “Missing Data as a Causal and Probabilistic Problem.” http://ftp.cs.ucla.edu/pub/stat_ser/r454.pdf.
Shpitser, Ilya, and Eric Tchetgen Tchetgen. 2014. “Causal Inference with a Graphical Hierarchy of Interventions.” November 8, 2014. http://arxiv.org/abs/1411.2127.
Vansteelandt, Stijn, Maarten Bekaert, and Gerda Claeskens. 2012. “On Model Selection and Model Misspecification in Causal Inference.” Statistical Methods in Medical Research 21 (1): 7–30. https://doi.org/10.1177/0962280210387717.
Yadav, Pranjul, Lisiane Prunelli, Alexander Hoff, Michael Steinbach, Bonnie Westra, Vipin Kumar, and Gyorgy Simon. 2016. “Causal Inference in Observational Data.” November 14, 2016. http://arxiv.org/abs/1611.04660.
Zander, Benito van der, Johannes Textor, and Maciej Liskiewicz. 2015. “Efficiently Finding Conditional Instruments for Causal Inference.” In Proceedings of the 24th International Conference on Artificial Intelligence, 3243–49. IJCAI’15. Buenos Aires, Argentina: AAAI Press. https://www.ijcai.org/Proceedings/15/Papers/457.pdf.
Zhang, Rui, Masaaki Imaizumi, Bernhard Schölkopf, and Krikamol Muandet. 2021. “Maximum Moment Restriction for Instrumental Variable Regression.” February 12, 2021. http://arxiv.org/abs/2010.07684.

No comments yet. Why not leave one?

GitHub-flavored Markdown & a sane subset of HTML is supported.