Causal inference on DAGs

Confounding! This scientist performed a miracle graph surgery intervention and you won’t believe what happened next

Making valid statistical inference, in the sense of making inference that is compatible with our understanding of the causal relationships that exist in the world (not just the correlations in our data). Graphical models and related techniques for doing it. Avoiding the danger of folk statistics. Observational studies, confounding, adjustment criteria, d-separation, identifiability, interventions, moral equivalence… Avoidance of Ecological fallacy/ Simpson’s paradox.

The gold standard, of course, is to work out if A causes B by doing an experiment where no input but A changes, then observing B, which is what a controlled trial is. In practice this is unattainable because it would usually require cloning the entire state of the universe and running multiple copies in parallel. Statistically it can be nearly as good to do the experiment where we change A and all other influences apart from are at least uncorrelated with A, which is more usually what we do — a randomised controlled trial. In many circumstances though, (budget restrictions, ethical constraints, bad experimental design…) we cannot do these ideal experiments, and a mathematical crutch is needed to get us the next-best outcome, which is to control for the things that we must (and not control for the things we must not).

Control trials are the gold standard but are not always feasible. From Girl Genius

In classic-flavoured causal inference, we use graphical models with the additional assumption that \(A\rightarrow B\) may be read as “A causes a change in B”. This is what you end up with if you use a Structural Equation Model (a.k.a. hierarchical models) to impose a causal structure on the observations. The result is a particular type of graph, a Directed Acyclic Graph_ (DAG) which, informally put, summarises what can possibly affect what in the model. Slightly more formally, it summarises what cannot (conditionally) affect what. C&C conditional treatment effect estimation by potential outcomes.

With this tool in hand I can answer the question of when I can use my crappy observational data, collected without a good experimental design for whatever reason, to do interventional inference? There is a lot of research in this area; I should summarise the salient bits for myself.

What can go wrong?

Inferring the optimal intervention requires accounting for which arrows are independent of which.

What can I actually identify? For a start, if we are resorting to this more difficult methodology that already suggests that we might be trying to use data which was collected with no regard to our actual statistical needs, and thus we might really stretch to imagine that we can actually find actual appropriate instruments in the data. Here is an essay on that theme.


Yanir Seroussi’s Causal inference resources recommends

Miguel Hernán and Jamie Robins’ causal inference book (Miguel A. Hernán and Robins 2020) is available in free draft form online. See Yanir Seroussi’s review.

Jonas Peters’ notes from his teaching in 2015 (I think I took this course).

Samantha Kleinberg wrote two classes, introductory and advanced. The latter is notable for handling for time-dependent causality.

Tutorial: David Sontag and Uri Shalit, Causal inference from observational studies. Mastering Metrics: The Path from Cause to Effect A resource list for causality in statistics, data science and physics.

Pearl’s do calculus

Brady Neal’s Introduction to Causal Inference includes his draft textbook.

Felix Elwert’s summary. (Elwert 2013)

Chapter 3 of (some edition of) Pearl’s book is available as an author’s preprint: Part 1, 2, 3, 4, 5, 6.

Stanford encyclopaedia of philosophy entry.

Various classic introductions (Pearl 2012, 1998; Elwert 2013; Morgan and Winship 2015; Rohrer 2018). Notably not recommended as a pedagogic experience (Koller and Friedman 2009) (although as a reference text it is great and will make you smarter).

The dagitty intro is an interactive guide via visualizations. Likewise, the ggdag bias structure vignette shows of the useful explanation diagrams available in ggdag and is also a good introduction to selection bias and causal DAGs themselves.

Amit Sharma’s tutorial at KDD. See also Emily Riederer’s Causal design patterns for data analysts Spurious correlation induced by sampling bias.

Still confused? Overwhelmed? I am. How about a diagram?

Instrumental variables

See instrumental variables.


Aalen, Odd O, K Røysland, Jm Gran, R Kouyos, and T Lange. 2016. Can We Believe the DAGs? A Comment on the Relationship Between Causal DAGs and Mechanisms.” Statistical Methods in Medical Research 25 (5): 2294–314.
Achab, Massil, Emmanuel Bacry, Stéphane Gaïffas, Iacopo Mastromatteo, and Jean-Francois Muzy. 2017. Uncovering Causality from Multivariate Hawkes Integrated Cumulants.” In PMLR.
Allen, John-Mark A., Jonathan Barrett, Dominic C. Horsman, Ciarán M. Lee, and Robert W. Spekkens. 2017. Quantum Common Causes and Quantum Causal Models.” Physical Review X 7 (3): 031021.
Aragam, Bryon, Jiaying Gu, and Qing Zhou. 2017. Learning Large-Scale Bayesian Networks with the Sparsebn Package.” arXiv:1703.04025 [Cs, Stat], March.
Aral, Sinan, Lev Muchnik, and Arun Sundararajan. 2009. Distinguishing Influence-Based Contagion from Homophily-Driven Diffusion in Dynamic Networks.” Proceedings of the National Academy of Sciences 106 (51): 21544–49.
Arjovsky, Martin, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 2020. Invariant Risk Minimization.” arXiv.
Arnold, Barry C., Enrique Castillo, and Jose M. Sarabia. 1999. Conditional Specification of Statistical Models. Springer Science & Business Media.
Athey, Susan, and Stefan Wager. 2019. Estimating Treatment Effects with Causal Forests: An Application.” arXiv:1902.07409 [Stat], February.
Bahadori, Mohammad Taha, Krzysztof Chalupka, Edward Choi, Robert Chen, Walter F. Stewart, and Jimeng Sun. 2017. Neural Causal Regularization Under the Independence of Mechanisms Assumption.” arXiv:1702.02604 [Cs, 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.
Bareinboim, Elias, Jin Tian, and Judea Pearl. 2014. Recovering from Selection Bias in Causal and Statistical Inference. In AAAI, 2410–16.
Besserve, Michel, Arash Mehrjou, Rémy Sun, and Bernhard Schölkopf. 2019. Counterfactuals Uncover the Modular Structure of Deep Generative Models.” In arXiv:1812.03253 [Cs, Stat].
Blom, Tineke, Stephan Bongers, and Joris M. Mooij. 2020. Beyond Structural Causal Models: Causal Constraints Models.” In Uncertainty in Artificial Intelligence, 585–94. PMLR.
Blom, Tineke, and Joris M Mooij. 2020. “Robust Model Predictions via Causal Ordering.” In, 10.
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.
Bonchi, Francesco, Francesco Gullo, Bud Mishra, and Daniele Ramazzotti. 2018. Probabilistic Causal Analysis of Social Influence.” In Proceedings of the 27th ACM International Conference on Information and Knowledge Management, 1003–12. CIKM ’18. New York, NY, USA: ACM.
Bongers, Stephan, Patrick Forré, Jonas Peters, Bernhard Schölkopf, and Joris M. Mooij. 2020. Foundations of Structural Causal Models with Cycles and Latent Variables.” arXiv:1611.06221 [Cs, Stat], October.
Bongers, Stephan, and Joris M. Mooij. 2018. From Random Differential Equations to Structural Causal Models: The Stochastic Case.” arXiv:1803.08784 [Cs, Stat], March.
Bongers, Stephan, Jonas Peters, Bernhard Schölkopf, and Joris M. Mooij. 2016. Structural Causal Models: Cycles, Marginalizations, Exogenous Reparametrizations and Reductions.” arXiv:1611.06221 [Cs, Stat], November.
Bottou, Léon, Jonas Peters, Joaquin Quiñonero-Candela, Denis X. Charles, D. Max Chickering, Elon Portugaly, Dipankar Ray, Patrice Simard, and Ed Snelson. 2013. Counterfactual Reasoning and Learning Systems.” arXiv:1209.2355 [Cs, Math, Stat], July.
Braunstein, Alfredo, and Alessandro Ingrosso. 2016. Inference of Causality in Epidemics on Temporal Contact Networks.” Scientific Reports 6 (1): 27538.
Bright, Liam Kofi, Daniel Malinsky, and Morgan Thompson. 2016. Causally Interpreting Intersectionality Theory.” Philosophy of Science 83 (1): 60–81.
Brito, Carlos, and Judea Pearl. 2002. A New Identification Condition for Recursive Models With Correlated Errors.” Structural Equation Modeling: A Multidisciplinary Journal 9 (4): 459–74.
———. 2012. Generalized Instrumental Variables.” arXiv:1301.0560 [Cs], December.
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. 2013. Causal Statistical Inference in High Dimensions.” Mathematical Methods of Operations Research 77 (3): 357–70.
———. 2020. Invariance, Causality and Robustness.” Statistical Science 35 (3): 404–26.
Bühlmann, Peter, Markus Kalisch, and Lukas Meier. 2014. High-Dimensional Statistics with a View Toward Applications in Biology.” Annual Review of Statistics and Its Application 1 (1): 255–78.
Bühlmann, Peter, Jonas Peters, Jan Ernest, and Marloes Maathuis. 2014. Predicting Causal Effects in High-Dimensional Settings.”
Bühlmann, Peter, Philipp Rütimann, and Markus Kalisch. 2013. Controlling False Positive Selections in High-Dimensional Regression and Causal Inference.” Statistical Methods in Medical Research 22 (5): 466–92.
Chalak, Karim, and Halbert White. 2012. Causality, Conditional Independence, and Graphical Separation in Settable Systems.” Neural Computation 24 (7): 1611–68.
Chau, Siu Lun, Jean-François Ton, Javier González, Yee Whye Teh, and Dino Sejdinovic. 2021. BayesIMP: Uncertainty Quantification for Causal Data Fusion,” June.
Chaves, Rafael, Gabriela Barreto Lemos, and Jacques Pienaar. 2018. Causal Modeling the Delayed-Choice Experiment.” Physical Review Letters 120 (19): 190401.
Chen, B, and J Pearl. 2012. “Regression and Causation: A Critical Examination of Econometric Textbooks.”
Christiansen, Rune, Niklas Pfister, Martin Emil Jakobsen, Nicola Gnecco, and Jonas Peters. 2020. A Causal Framework for Distribution Generalization,” June.
Claassen, Tom, Joris M. Mooij, and Tom Heskes. 2014. Proof Supplement - Learning Sparse Causal Models Is Not NP-Hard (UAI2013).” arXiv:1411.1557 [Stat], November.
Colombo, Diego, Marloes H. Maathuis, Markus Kalisch, and Thomas S. Richardson. 2012. Learning High-Dimensional Directed Acyclic Graphs with Latent and Selection Variables.” The Annals of Statistics 40 (1): 294–321.
Cornish, Rob, Muhammad Faaiz Taufiq, Arnaud Doucet, and Chris Holmes. 2023. Causal Falsification of Digital Twins.” arXiv.
Dash, Denver. 2003. Caveats For Causal Reasoning With Equilibrium Models.”
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.
Didelez, Vanessa. n.d. Causal Reasoning for Events in Continuous Time: A Decision–Theoretic Approach.”
Duvenaud, David K., Daniel Eaton, Kevin P. Murphy, and Mark W. Schmidt. 2010. Causal Learning Without DAGs. In NIPS Causality: Objectives and Assessment, 177–90.
Eichler, Michael. 2001. Granger-Causality Graphs for Multivariate Time Series.” Granger-Causality Graphs for Multivariate Time Series.
Elwert, Felix. 2013. Graphical Causal Models.” In Handbook of Causal Analysis for Social Research, edited by Stephen L. Morgan, 245–73. Handbooks of Sociology and Social Research. Dordrecht: Springer Netherlands.
Entner, Doris, Patrik Hoyer, and Peter Spirtes. 2013. Data-Driven Covariate Selection for Nonparametric Estimation of Causal Effects.” In Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, 256–64.
Ernest, Jan, and Peter Bühlmann. 2014. Marginal Integration for Fully Robust Causal Inference.” arXiv:1405.1868 [Stat], May.
Fernández-Loría, Carlos, and Foster Provost. 2021. Causal Decision Making and Causal Effect Estimation Are Not the Same… and Why It Matters.” arXiv:2104.04103 [Cs, Stat], September.
Fixx, James F. 1977. Games for the superintelligent. London: Muller.
Foreman-Mackey, Daniel, Benjamin T. Montet, David W. Hogg, Timothy D. Morton, Dun Wang, and Bernhard Schölkopf. 2015. A Systematic Search for Transiting Planets in the K2 Data.” The Astrophysical Journal 806 (2): 215.
Fu, Fei, and Qing Zhou. 2013. Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent.” Journal of the American Statistical Association 108 (501): 288–300.
Gebharter, Alexander, and Nina Retzlaff. 2020. A New Proposal How to Handle Counterexamples to Markov Causation à La Cartwright, or: Fixing the Chemical Factory.” Synthese 197 (4): 1467–86.
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.
Gendron, Gaël, Michael Witbrock, and Gillian Dobbie. 2023. A Survey of Methods, Challenges and Perspectives in Causality.” arXiv.
Genewein, Tim, Tom McGrath, Grégoire Déletang, Vladimir Mikulik, Miljan Martic, Shane Legg, and Pedro A. Ortega. 2020. Algorithms for Causal Reasoning in Probability Trees.” arXiv:2010.12237 [Cs], October.
Geng, Zhi, Yue Liu, Chunchen Liu, and Wang Miao. 2019. Evaluation of Causal Effects and Local Structure Learning of Causal Networks.” Annual Review of Statistics and Its Application 6 (1): 103–24.
Glymour, Clark. 1998. What Went Wrong? Reflections on Science by Observation and the Bell Curve.” Philosophy of Science 65 (1): 1–32.
Gu, Jiaying, Fei Fu, and Qing Zhou. 2014. Adaptive Penalized Estimation of Directed Acyclic Graphs From Categorical Data.” arXiv:1403.2310 [Stat], March.
Guo, Siyuan, Viktor Tóth, Bernhard Schölkopf, and Ferenc Huszár. 2022. Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data.” arXiv.
Hansen, Niels, and Alexander Sokol. 2014. Causal Interpretation of Stochastic Differential Equations.” Electronic Journal of Probability 19.
Hernán, Miguel A. 2016. Does Water Kill? A Call for Less Casual Causal Inferences.” Annals of Epidemiology 26 (10): 674–80.
———. 2018. The C-Word: Scientific Euphemisms Do Not Improve Causal Inference From Observational Data.” American Journal of Public Health 108 (5): 616–19.
Hernán, Miguel A, and James M Robins. 2020. Causal Inference: What If.
Hernán, Miguel, and Jamie Robins. 2019a. Causal Inference Vol 3.
———. 2019b. Causal Inference Vol 2.
———. 2019c. Causal Inference Vol 1.
Hinton, Geoffrey E., Simon Osindero, and Kejie Bao. 2005. Learning Causally Linked Markov Random Fields.” In Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics, 128–35. Citeseer.
Hoyer, Patrik O., Dominik Janzing, Joris M Mooij, Jonas Peters, and Bernhard Schölkopf. 2009. Nonlinear Causal Discovery with Additive Noise Models.” In Advances in Neural Information Processing Systems 21, edited by D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, 689–96. Curran Associates, Inc.
Huang, Yuxiao, and Samantha Kleinberg. 2015. Fast and Accurate Causal Inference from Time Series Data.” In, 6.
Hult, Ludvig, and Dave Zachariah. 2020. Inference of Causal Effects When Adjustment Sets Are Unknown.” arXiv:2012.08154 [Cs, Stat], December.
Hyttinen, Antti, Frederick Eberhardt, and Matti Järvisalo. n.d. Do-Calculus When the True Graph Is Unknown.”
Imbens, Guido, and Konrad Menzel. 2021. A Causal Bootstrap.” The Annals of Statistics 49 (3): 1460–88.
Janzing, Dominik, Joris Mooij, Kun Zhang, Jan Lemeire, Jakob Zscheischler, Povilas Daniušis, Bastian Steudel, and Bernhard Schölkopf. 2012. Information-Geometric Approach to Inferring Causal Directions.” Artificial Intelligence 182-183 (May): 1–31.
Janzing, Dominik, and Bernhard Schölkopf. 2010. Causal Inference Using the Algorithmic Markov Condition.” IEEE Transactions on Information Theory 56 (10): 5168–94.
Johansson, Fredrik D., Uri Shalit, and David Sontag. 2018. Learning Representations for Counterfactual Inference.” arXiv:1605.03661 [Cs, Stat], June.
Johansson, Fredrik, Uri Shalit, and David Sontag. 2016. Learning Representations for Counterfactual Inference.” In International Conference on Machine Learning, 3020–29. PMLR.
Jordan, Michael Irwin. 1999. Learning in Graphical Models. Cambridge, Mass.: MIT Press.
Jordan, Michael I., Yixin Wang, and Angela Zhou. 2022. Empirical Gateaux Derivatives for Causal Inference.” arXiv.
Jordan, Michael I., and Yair Weiss. 2002a. Graphical Models: Probabilistic Inference.” The Handbook of Brain Theory and Neural Networks, 490–96.
———. 2002b. Probabilistic Inference in Graphical Models.” Handbook of Neural Networks and Brain Theory.
Kalainathan, Diviyan, Olivier Goudet, and Ritik Dutta. 2020. Causal Discovery Toolbox: Uncovering Causal Relationships in Python.” Journal of Machine Learning Research 21 (37): 1–5.
Kalisch, Markus, and Peter Bühlmann. 2007. Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm.” Journal of Machine Learning Research 8 (May): 613–36.
Kallus, Nathan. 2020. Generalized Optimal Matching Methods for Causal Inference.” Journal of Machine Learning Research 21 (62): 1–54.
Kennedy, Edward H. 2015. Semiparametric Theory and Empirical Processes in Causal Inference.” arXiv Preprint arXiv:1510.04740.
Kilbertus, Niki, Mateo Rojas Carulla, Giambattista Parascandolo, Moritz Hardt, Dominik Janzing, and Bernhard Schölkopf. 2017. Avoiding Discrimination Through Causal Reasoning.” In Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 656–66. Curran Associates, Inc.
Kim, Jin H., and Judea Pearl. 1983. A Computational Model for Causal and Diagnostic Reasoning in Inference Systems. In IJCAI, 83:190–93. San Francisco, CA, USA: Citeseer.
Kleinberg, Samantha. 2012. Causality, Probability, and Time. 1 edition. Cambridge: Cambridge University Press.
———. 2015. Why: A Guide to Finding and Using Causes. 1st edition. Beijing ; Boston: O’Reilly Media.
Kocaoglu, Murat, Christopher Snyder, Alexandros G. Dimakis, and Sriram Vishwanath. 2017. CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training.” arXiv:1709.02023 [Cs, Math, Stat], September.
Kohavi, Ron, Diane Tang, and Ya Xu. 2020. Trustworthy Online Controlled Experiments: A Practical Guide to A/B Testing. 1st edition. Cambridge, United Kingdom ; New York, NY: Cambridge University Press.
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.
Koller, Daphne, and Nir Friedman. 2009. Probabilistic Graphical Models : Principles and Techniques. Cambridge, MA: MIT Press.
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.
Lauritzen, S. L., and D. J. Spiegelhalter. 1988. Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems.” Journal of the Royal Statistical Society. Series B (Methodological) 50 (2): 157–224.
Lauritzen, Steffen L. 1996. Graphical Models. Oxford Statistical Science Series. Clarendon Press.
———. 2000. Causal Inference from Graphical Models.” In Complex Stochastic Systems, 63–107. CRC Press.
Lee, Sanghack, and Elias Bareinboim. 2021. Causal Identification with Matrix Equations.” In.
———. n.d. “Causal Effect Identifiability Under Partial-Observability,” 10.
Locatello, Francesco, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, and Olivier Bachem. 2019. Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations.” arXiv:1811.12359 [Cs, Stat], June.
Lopez-Paz, David, Robert Nishihara, Soumith Chintala, Bernhard Schölkopf, and Léon Bottou. 2016. Discovering Causal Signals in Images.” arXiv:1605.08179 [Cs, Stat], May.
Louizos, Christos, Uri Shalit, Joris M Mooij, David Sontag, Richard Zemel, and Max Welling. 2017. Causal Effect Inference with Deep Latent-Variable Models.” In Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 6446–56. Curran Associates, Inc.
Maathuis, Marloes H., and Diego Colombo. 2013. A Generalized Backdoor Criterion.” arXiv Preprint arXiv:1307.5636.
Maathuis, Marloes H., Diego Colombo, Markus Kalisch, and Peter Bühlmann. 2010. Predicting Causal Effects in Large-Scale Systems from Observational Data.” Nature Methods 7 (4): 247–48.
Maathuis, Marloes H., Markus Kalisch, and Peter Bühlmann. 2009. Estimating High-Dimensional Intervention Effects from Observational Data.” The Annals of Statistics 37 (6A): 3133–64.
Malinsky, Daniel, Ilya Shpitser, and Thomas Richardson. 2019. A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects.” arXiv:1903.03662 [Stat], March.
Marbach, Daniel, Robert J. Prill, Thomas Schaffter, Claudio Mattiussi, Dario Floreano, and Gustavo Stolovitzky. 2010. Revealing Strengths and Weaknesses of Methods for Gene Network Inference.” Proceedings of the National Academy of Sciences 107 (14): 6286–91.
Meinshausen, Nicolai. 2018. Causality from a Distributional Robustness Point of View.” In 2018 IEEE Data Science Workshop (DSW), 6–10.
Messerli, Franz H. 2012. Chocolate Consumption, Cognitive Function, and Nobel Laureates.” New England Journal of Medicine 367 (16): 1562–64.
Mihalkova, Lilyana, and Raymond J. Mooney. 2007. Bottom-up Learning of Markov Logic Network Structure.” In Proceedings of the 24th International Conference on Machine Learning, 625–32. ACM.
Mogensen, Søren Wengel, Daniel Malinsky, and Niels Richard Hansen. 2018. Causal Learning for Partially Observed Stochastic Dynamical Systems.” In UAI2018, 17.
Montanari, Andrea. 2011. Lecture Notes for Stat 375 Inference in Graphical Models.”
Mooij, Joris M., Jonas Peters, Dominik Janzing, Jakob Zscheischler, and Bernhard Schölkopf. 2016. Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks.” Journal of Machine Learning Research 17 (32): 1–102.
Morgan, Stephen L., and Christopher Winship. 2015. Counterfactuals and Causal Inference. Cambridge University Press.
Msaouel, Pavlos. 2022. The Big Data Paradox in Clinical Practice.” Cancer Investigation 40 (7): 1–10.
Murphy, Kevin P. 2012. Machine learning: a probabilistic perspective. 1 edition. Adaptive computation and machine learning series. Cambridge, MA: MIT Press.
Murray, Eleanor J., Sonja A. Swanson, and Miguel A. Hernán. 2019. Guidelines for Estimating Causal Effects in Pragmatic Randomized Trials.” arXiv:1911.06030 [Stat], November.
Neal, Brady. 2020. Introduction to Causal Inference from a Machine Learning Perspective.” Course Lecture Notes (Draft).
Neapolitan, Richard E. 2003. Learning Bayesian Networks. Vol. 38. Prentice Hal, Paperback.
Ng, Ignavier, Zhuangyan Fang, Shengyu Zhu, Zhitang Chen, and Jun Wang. 2020. Masked Gradient-Based Causal Structure Learning.” arXiv:1910.08527 [Cs, Stat], February.
Ng, Ignavier, Shengyu Zhu, Zhitang Chen, and Zhuangyan Fang. 2019. A Graph Autoencoder Approach to Causal Structure Learning.” In Advances In Neural Information Processing Systems.
Nilsson, Anton, Carl Bonander, Ulf Strömberg, and Jonas Björk. 2021. A Directed Acyclic Graph for Interactions.” International Journal of Epidemiology 50 (2): 613–19.
Noel, Hans, and Brendan Nyhan. 2011. The ‘Unfriending’ Problem: The Consequences of Homophily in Friendship Retention for Causal Estimates of Social Influence.” Social Networks 33 (3): 211–18.
Ortega, Pedro A., Markus Kunesch, Grégoire Delétang, Tim Genewein, Jordi Grau-Moya, Joel Veness, Jonas Buchli, et al. 2021. Shaking the Foundations: Delusions in Sequence Models for Interaction and Control.” arXiv:2110.10819 [Cs], October.
Pearl, Judea. 1982. Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach.” In Proceedings of the Second AAAI Conference on Artificial Intelligence, 133–36. AAAI’82. Pittsburgh, Pennsylvania: AAAI Press.
———. 1986. Fusion, Propagation, and Structuring in Belief Networks.” Artificial Intelligence 29 (3): 241–88.
———. 1998. Graphical Models for Probabilistic and Causal Reasoning.” In Quantified Representation of Uncertainty and Imprecision, edited by Philippe Smets, 367–89. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Dordrecht: Springer Netherlands.
———. 2008. Probabilistic reasoning in intelligent systems: networks of plausible inference. Rev. 2. print., 12. [Dr.]. The Morgan Kaufmann series in representation and reasoning. San Francisco, Calif: Kaufmann.
———. 2009a. Causal Inference in Statistics: An Overview.” Statistics Surveys 3: 96–146.
———. 2009b. Causality: Models, Reasoning and Inference. Cambridge University Press.
———. 2010. The Foundations of Causal Inference.” Sociological Methodology 40 (1): 75–149.
———. 2011. Simpson’s Paradox: An Anatomy.”
———. 2012. “The Do-Calculus Revisited Judea Pearl Keynote Lecture, August 17, 2012 UAI-2012 Conference, Catalina, CA.” Edited by Nando de Freitas and Kevin Murphy, 8.
Pearl, Judea, and Elias Bareinboim. 2014. External Validity: From Do-Calculus to Transportability Across Populations.” Statistical Science 29 (4): 579–95.
Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell. 2016. Causal Inference in Statistics: A Primer. Wiley.
Peters, Jonas. 2015. Causality Lecture Notes.”
Peters, Jonas, Peter Bühlmann, and Nicolai Meinshausen. 2015. Causal Inference Using Invariant Prediction: Identification and Confidence Intervals.” arXiv:1501.01332 [Stat], January.
Peters, Jonas, Dominik Janzing, and Bernhard Schölkopf. 2017. Elements of Causal Inference: Foundations and Learning Algorithms. Adaptive Computation and Machine Learning Series. Cambridge, Massachuestts: The MIT Press.
Peters, Jonas, Joris M. Mooij, Dominik Janzing, and Bernhard Schölkopf. 2014. “Causal Discovery with Continuous Additive Noise Models.” The Journal of Machine Learning Research 15 (1): 2009–53.
Raginsky, M. 2011. Directed Information and Pearl’s Causal Calculus.” In 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 958–65.
Rakesh, Vineeth, Ruocheng Guo, Raha Moraffah, Nitin Agarwal, and Huan Liu. 2018. Linked Causal Variational Autoencoder for Inferring Paired Spillover Effects.” In Proceedings of the 27th ACM International Conference on Information and Knowledge Management, 1679–82. CIKM ’18. New York, NY, USA: Association for Computing Machinery.
Rehkopf, David H., M. Maria Glymour, and Theresa L. Osypuk. 2016. The Consistency Assumption for Causal Inference in Social Epidemiology: When a Rose Is Not a Rose.” Current Epidemiology Reports 3 (1): 63–71.
Richardson, Thomas S., and James M. Robins. 2013. Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality.” Citeseer.
Richardson, Thomas, and Peter Spirtes. 2002. Ancestral Graph Markov Models.” Annals of Statistics 30 (4): 962–1030.
Robins, James M. 1997. Causal Inference from Complex Longitudinal Data.” In Latent Variable Modeling and Applications to Causality, edited by Maia Berkane, 69–117. Lecture Notes in Statistics. New York, NY: Springer.
Rohrer, Julia M. 2018. Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data: Advances in Methods and Practices in Psychological Science, January.
Rothenhäusler, Dominik, Nicolai Meinshausen, Peter Bühlmann, and Jonas Peters. 2020. Anchor Regression: Heterogeneous Data Meets Causality.” arXiv:1801.06229 [Stat], May.
Rotnitzky, Andrea, and Ezequiel Smucler. 2020. Efficient Adjustment Sets for Population Average Causal Treatment Effect Estimation in Graphical Models.” Journal of Machine Learning Research 21 (188): 1–86.
Rubenstein, Paul K., Stephan Bongers, Bernhard Schölkopf, and Joris M. Mooij. 2018. From Deterministic ODEs to Dynamic Structural Causal Models.” In Uncertainty in Artificial Intelligence.
Rubenstein, Paul K., Sebastian Weichwald, Stephan Bongers, Joris M. Mooij, Dominik Janzing, Moritz Grosse-Wentrup, and Bernhard Schölkopf. 2017. Causal Consistency of Structural Equation Models.” arXiv:1707.00819 [Cs, Stat], July.
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.
Sauer, Brian, and Tyler J. VanderWeele. 2013. Use of Directed Acyclic Graphs. Agency for Healthcare Research and Quality (US).
Schölkopf, Bernhard. 2022. Causality for Machine Learning.” In Probabilistic and Causal Inference: The Works of Judea Pearl, 1st ed., 36:765–804. New York, NY, USA: Association for Computing Machinery.
Schölkopf, Bernhard, David W. Hogg, Dun Wang, Daniel Foreman-Mackey, Dominik Janzing, Carl-Johann Simon-Gabriel, and Jonas Peters. 2015. Removing Systematic Errors for Exoplanet Search via Latent Causes.” arXiv:1505.03036 [Astro-Ph, Stat], May.
Schölkopf, Bernhard, Dominik Janzing, Jonas Peters, Eleni Sgouritsa, Kun Zhang, and Joris Mooij. 2012. On Causal and Anticausal Learning.” In ICML 2012.
Schölkopf, Bernhard, Francesco Locatello, Stefan Bauer, Nan Rosemary Ke, Nal Kalchbrenner, Anirudh Goyal, and Yoshua Bengio. 2021. Toward Causal Representation Learning.” Proceedings of the IEEE 109 (5): 612–34.
Schölkopf, Bernhard, Krikamol Muandet, Kenji Fukumizu, and Jonas Peters. 2015. Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations.” arXiv:1501.06794 [Cs, Stat], January.
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.
Shalizi, Cosma Rohilla, and Edward McFowland III. 2016. Controlling for Latent Homophily in Social Networks Through Inferring Latent Locations.” arXiv:1607.06565 [Physics, Stat], July.
Shalizi, Cosma Rohilla, and Andrew C. Thomas. 2011. Homophily and Contagion Are Generically Confounded in Observational Social Network Studies.” Sociological Methods & Research 40 (2): 211–39.
Sharma, Amit, and Emre Kiciman. 2020. DoWhy: An End-to-End Library for Causal Inference.” arXiv.
Shipley, Bill. 2016. Cause and Correlation in Biology: A User’s Guide to Path Analysis, Structural Equations and Causal Inference with R. 2nd ed. Cambridge: Cambridge University Press.
Shpitser, Ilya, and Judea Pearl. 2008. “Complete Identification Methods for the Causal Hierarchy.” The Journal of Machine Learning Research 9: 1941–79.
Shpitser, Ilya, and Eric Tchetgen Tchetgen. 2014. Causal Inference with a Graphical Hierarchy of Interventions.” arXiv:1411.2127 [Stat], November.
Shrier, Ian, and Robert W. Platt. 2008. Reducing Bias Through Directed Acyclic Graphs.” BMC Medical Research Methodology 8 (1): 70.
Smith, Bonnie, Elizabeth L. Ogburn, Matt McGue, Saonli Basu, and Daniel O. Scharfstein. 2020. Causal Effects in Twin Studies: The Role of Interference.” arXiv:2007.04511 [Stat], July.
Smith, David A., and Jason Eisner. 2008. Dependency Parsing by Belief Propagation.” In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 145–56. Association for Computational Linguistics.
Spirtes, Peter, Clark Glymour, and Richard Scheines. 2001. Causation, Prediction, and Search. Second Edition. Adaptive Computation and Machine Learning. The MIT Press.
Subbaswamy, Adarsh, Peter Schulam, and Suchi Saria. 2019. Preventing Failures Due to Dataset Shift: Learning Predictive Models That Transport.” In The 22nd International Conference on Artificial Intelligence and Statistics, 3118–27. PMLR.
Suzuki, Etsuji, Tomohiro Shinozaki, and Eiji Yamamoto. 2020. Causal Diagrams: Pitfalls and Tips.” Journal of Epidemiology 30 (4): 153–62.
Textor, Johannes, Alexander Idelberger, and Maciej Liśkiewicz. 2015. Learning from Pairwise Marginal Independencies.” arXiv:1508.00280 [Cs], August.
Textor, Johannes, and Maciej Liśkiewicz. 2011. Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective.” In Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, 681–88. UAI’11. Arlington, Virginia, USA: AUAI Press.
Tschantz, Michael Carl, Shayak Sen, and Anupam Datta. 2019. Differential Privacy as a Causal Property.” arXiv:1710.05899 [Cs], July.
Tu, Ruibo, Cheng Zhang, Paul Ackermann, Hedvig Kjellström, and Kun Zhang. 2018. Causal Discovery in the Presence of Missing Data.” arXiv:1807.04010 [Cs, Stat], July.
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.
Veitch, Victor, and Anisha Zaveri. 2020. Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding,” March.
Visweswaran, Shyam, and Gregory F. Cooper. 2014. Counting Markov Blanket Structures.” arXiv:1407.2483 [Cs, Stat], July.
Walker, Jeffrey A. 2014. The Effect of Unmeasured Confounders on the Ability to Estimate a True Performance or Selection Gradient (and Other Partial Regression Coefficients).” Evolution 68 (7): 2128–36.
Wang, Dun, David W. Hogg, Daniel Foreman-Mackey, and Bernhard Schölkopf. 2017. A Pixel-Level Model for Event Discovery in Time-Domain Imaging.” arXiv:1710.02428 [Astro-Ph], October.
Wang, Yuhao, Liam Solus, Karren Dai Yang, and Caroline Uhler. 2017. Permutation-Based Causal Inference Algorithms with Interventions,” May.
Weichwald, Sebastian, and Jonas Peters. 2020. Causality in Cognitive Neuroscience: Concepts, Challenges, and Distributional Robustness.” arXiv:2002.06060 [q-Bio, Stat], July.
Westfall, Jacob, and Tal Yarkoni. 2016. Statistically Controlling for Confounding Constructs Is Harder Than You Think.” PLOS ONE 11 (3): e0152719.
Wong, Jeffrey C. 2020. Computational Causal Inference.” arXiv:2007.10979 [Cs, Stat], July.
Wright, Sewall. 1934. The Method of Path Coefficients.” The Annals of Mathematical Statistics 5 (3): 161–215.
Yadav, Pranjul, Lisiane Prunelli, Alexander Hoff, Michael Steinbach, Bonnie Westra, Vipin Kumar, and Gyorgy Simon. 2016. Causal Inference in Observational Data.” arXiv:1611.04660 [Cs, Stat], November.
Yang, Mengyue, Furui Liu, Zhitang Chen, Xinwei Shen, Jianye Hao, and Jun Wang. 2020. CausalVAE: Disentangled Representation Learning via Neural Structural Causal Models.” arXiv:2004.08697 [Cs, Stat], July.
Yedidia, J.S., W.T. Freeman, and Y. Weiss. 2003. Understanding Belief Propagation and Its Generalizations.” In Exploring Artificial Intelligence in the New Millennium, edited by G. Lakemeyer and B. Nebel, 239–36. Morgan Kaufmann Publishers.
Zander, Benito van der, and Maciej Liśkiewicz. 2016. Separators and Adjustment Sets in Markov Equivalent DAGs.” In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, 3315–21. AAAI’16. Phoenix, Arizona: AAAI Press.
Zander, Benito van der, Maciej Liśkiewicz, and Johannes Textor. 2014. Constructing Separators and Adjustment Sets in Ancestral Graphs.” In Proceedings of the UAI 2014 Conference on Causal Inference: Learning and Prediction - Volume 1274, 11–24. CI’14. Aachen, DEU:
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.
Zhang, Kun, Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. 2012. Kernel-Based Conditional Independence Test and Application in Causal Discovery.” arXiv:1202.3775 [Cs, Stat], February.
Zheng, Xun, Bryon Aragam, Pradeep K Ravikumar, and Eric P Xing. 2018. DAGs with NO TEARS: Continuous Optimization for Structure Learning.” In Advances in Neural Information Processing Systems 31, edited by S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, 31:9472–83. Curran Associates, Inc.

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