Pennsylvania State University

Note: The study guide (including slides) are updated AFTER the corresponding lecture(s)

Course overview. History of causal inference. What is a cause? Why study causal inference? Causation versus association; seeing, versus doing, imagining. Why data are not always enough for drawing sound causal conclusions. Pitfalls of inference from observational data. Potential outcomes framwork. Causation versus Association. Measures of Association. Examples.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Chapter 1, Pearl, J., Glymour, M. and Jewell, N.P., 2016. Causal inference in statistics: A primer. John Wiley & Sons.
• Watch: Judea Pearl, The New Science of Cause and Effect
• Read: Hernan, M. and Robins, J.M., Chapter 1, Chapter 2. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.

Recommended Materials

• Read: Hernan, M.A., Hsu, J. and Healy, B. (2019).A Second Chance to Get Causal Inference Right: A Classification of Data Science Tasks 32(1), pp.42-49.
• Read: Pearl, J., 1997. The new challenge: From a century of statistics to the age of causation. In: Computing Science and Statistics (pp. 415-423).

Causation versus association. What is a causal effect? Potential Outcomes framework. Randomized experiments. Estimating causal effects. Inferring causation from association under identifiability assumptions. Exchangeability, positivity, consistency. Randomized experiments revisited. Stratified or Conditionally randomized experiments. Paired Randomized experiments. The power of randomization.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 2, Chapter 3. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.

Recommended Materials

• Read: Hernan, M.A., Hsu, J. and Healy, B. (2019).A Second Chance to Get Causal Inference Right: A Classification of Data Science Tasks 32(1), pp.42-49.
• Read: Rubin, D. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association 100.469 (2005): 322-331.

Effect estimation. Confidence intervals and p-values.

Effect modification. Why do we care about effect modification? Stratification to identify effect modification. Stratification as a form of adjustment. Matching as a form of adjustment. Effect modification and adjustment methods. Interaction among interventions. Identifying interactions. Counterfactual response types and interactions.

Review of probability theory. Independence and conditional independence. Bayesian networks.

Required Materials

• Review: Honavar, V. Lecture Slides
• Review: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 1.
• Read: Hernan, M. and Robins, J.M., Chapter 4, Chapter5. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 2.

Recommended Materials

• Elwert, F. (2013). Graphical causal models. In Handbook of causal analysis for social research (pp. 245-273). Springer, Dordrecht.

Semantics of Bayes networks. d-separation - graphical criterion for conditional independence. From Bayes networks to Causal Bayes Networks or Structural Causal Models. Causal effects as interventions. The do operator.

A short detour on expectation, law of unconscious statistician, law of iterated expectation. Regression revisited.

Linear causal models

Why doing (intervention) is not the same as seeing (observation) - structural causal models perspective and regression perspective. Identifying causal effects.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 6, Chapter 7. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 3.
• Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapter 3.

Recommended Materials

• Elwert, F. (2013). Graphical causal models. In Handbook of causal analysis for social research (pp. 245-273). Springer, Dordrecht.

Confounding. Identifying causal effects in the presence of confounding. The backdoor criterion (BDC) for identifying the variables to control for. Special cases of BDC: Parents of treatment, parents of outcome, joint ancestors (of treatment and outcome), and confounder selection criteria. Confounding through the lens of causal calculus. Pitfalls of traditional statistical, epidemiological and other criteria for confounder identification. Limitations of BDC. Limitations of the Back-door criterion. Front-door (FDC) criterion for identifying causal effects. Modularity of interventional distributions and BDC and FDC viewed through the lens of modularity.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 6, Chapter 7. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 3.
• Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapters 4 and 6.

Recommended Materials

• Dablander, F. (2020, February 13). An Introduction to Causal Inference. https://doi.org/10.31234/osf.io/b3fkw
• Judea, Pearl. An introduction to causal inference.The International Journal of Biostatistics 6, no. 2 (2010): 1-62.

Do-calculus and causal identifiability. 3 rules of do-calculus. Examples of causal effect identification using do-calculus. Identifiability of fully observable Causal Models. Conditions under which a causal model is unidentifiable from observational data. Completeness of do-calculus for causal effect identification.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 6, Chapter 7. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 3.
• Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapters 4 and 6.

Recommended Materials

• Dablander, F. (2020, February 13). An Introduction to Causal Inference. https://doi.org/10.31234/osf.io/b3fkw
• Judea, Pearl. An introduction to causal inference.The International Journal of Biostatistics 6, no. 2 (2010): 1-62.
• Shpitser, I. and Pearl, J., 2008. Complete identification methods for the causal hierarchy. Journal of Machine Learning Research, 9, pp.1941-1979.
• Tian, Jin, and Judea Pearl. A general identification condition for causal effects. In Eighteenth national conference on Artificial intelligence, pp. 567-573. 2002.

Linear causal models. Linear regression revisited. Linear structural causal models. Regression coefficients versus structural coefficients. Path analysis. Identifying causal effects in linear causal models. Algorithms for identifying causal effects from linear causal moedls

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 3, Section 3.8
• Chen, Bryant, and Judea Pearl. Graphical tools for linear structural equation modeling. (2014).
• Pearl, J., 1998. Graphs, causality, and structural equation models. Sociological Methods & Research, 27(2), pp.226-284.

Recommended Materials

• Wright, S. (1934). The method of path coefficients. The annals of mathematical statistics, 5(3), 161-215.
• Tian, Jin. Identifying direct causal effects in linear models. In Proceedings of the National Conference on Artificial Intelligence, vol. 20, no. 1, p. 346. Menlo Park, CA; Cambridge, MA; London; AAAI Press; MIT Press; 1999, 2005.
• Pearl. J. (2013). < ahref="./pearllinear.pdf">Linear Models: A Useful“Microscope” for Causal Analysis.. Journal of Causal Inference 2013; 1(1): 155–170
• Kumor, Daniel, Bryant Chen, and Elias Bareinboim. Efficient identification in linear structural causal models with instrumental cutsets. Advances in Neural Information Processing Systems 32 (2019).
• Kumor, D., Cinelli, C., & Bareinboim, E. (2020, November). Efficient identification in linear structural causal models with auxiliary cutsets. In International Conference on Machine Learning (pp. 5501-5510). PMLR.

Counterfactuals as causal effects that cannot be expressed using the do-operator. Defining and computing counterfactuals. Structural interpretation of counterfactuals. Fundamental law of counterfactuals. Using population data along with structural causal model to infer individual behavior. 3-step procedure for computing counterfactuals. Non-deterministic counterfactuals. Graphical representation of counterfactuals. Causal effects of treatment on the treated.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 6, Chapter 7. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 4.

Recommended Materials

• Galles, D., and Pearl, J. (1998). An axiomatic characterization of causal counterfactuals. Foundations of Science 3 (1998): 151-182.
• Pearl, J. (2013). Structural counterfactuals: A brief introduction. Cognitive science, 37(6), pp.977-985. Corrections
• Shpitser, I., and Pearl, J. (2007) What counterfactuals can be tested. In 23rd Conference on Uncertainty in Artificial Intelligence, UAI 2007, pp. 352-359.
• Balke, A. and Pearl, J. (1995). Counterfactuals and policy analysis in structural models. In Proceedings of the Eleventh conference on Uncertainty in artificial intelligence, pp. 11-18.

Path disabling interventions. Counterfactual definitions of direct and indirect causal effects - Total effect, controlled direct effect, natural direct effect, natural indirect effect, conditions for identifying natural effects.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 6, Chapter 7. Causal Inference: What if. Boca Raton: Chapman and Hill/CRC, 2020.
• Read: Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics. A primer. Chapter 4.

Recommended Materials

• Pearl, Judea. Interpretation and identification of causal mediationPsychological methods 19, no. 4 (2014): 459.
• Shpitser, I., 2013. Counterfactual graphical models for longitudinal mediation analysis with unobserved confounding. Cognitive science, 37(6), pp.1011-1035.
• Shpitser, I. and Pearl, J., 2012. Effects of treatment on the treated: Identification and generalization. arXiv preprint arXiv:1205.2615.
• Shpitser, I., & VanderWeele, T. J. (2011). A complete graphical criterion for the adjustment formula in mediation analysis. The international journal of biostatistics, 7(1), 16. https://doi.org/10.2202/1557-4679.1297

Causal effect estimation. Review of identifiability conditions. Estimation of causal effects from observational studies as an exercise in extracting mini randomized experiments from observational data. Conditional outcome models (COM) and grouped COM (GCOM) model. TARnet and X-Learner. Estimating the assignment mechanism - propensity scores. Inverse propensity score weighting. Ensuring exchangeability - covariate balance (matching, stratification, etc.). Combining COM and propensity scores. Regression.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Hernan, M. and Robins, J.M., Chapter 10.
• Read: Rubin, D. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association 100.469 (2005): 322-331.
• Read: Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapter 7.

Recommended Materials

• Austin, P. C. An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate behavioral research 46.3 (2011): 399-424.
• Stuart, E.A., 2010. Matching methods for causal inference: A review and a look forward. Statistical science: a review journal of the Institute of Mathematical Statistics, 25(1), p.1.
• Westreich, D., Lessler, J. and Funk, M.J., 2010. Propensity score estimation: neural networks, support vector machines, decision trees (CART), and meta-classifiers as alternatives to logistic regression. Journal of clinical epidemiology, 63(8), pp.826-833.
• Josey, K.P., Juarez‐Colunga, E., Yang, F. and Ghosh, D., 2020. A framework for covariate balance using Bregman distances. Scandinavian Journal of Statistics.
• Imai, Kosuke, and Marc Ratkovic. Covariate balancing propensity score. Journal of the Royal Statistical Society: Series B: Statistical Methodology (2014): 243-263.
• Künzel, S.R., Sekhon, J.S., Bickel, P.J. and Yu, B., 2019. Metalearners for estimating heterogeneous treatment effects using machine learning. Proceedings of the national academy of sciences, 116(10), pp.4156-4165.
• Shalit, Uri, Fredrik D. Johansson, and David Sontag. Estimating individual treatment effect: generalization bounds and algorithms.. In International Conference on Machine Learning, pp. 3076-3085. PMLR, 2017.

Causal effect estimation (continued). Doubly robust methods for causal effect estimation. Covariate balancing propensity scores. Sample and covariate reweighting. Subspace methods. Tree-based methods: CART, BART, and Causal Forests. Representation learning methods for causal effect estimation. Learning counterfactual representations. Learning covariate balanced representations. Estimating individual treatment effects using generative adversarial networks. Causal effect estimation using Double machine learning.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapter 7.
• Read: Koch, B.J., Sainburg, T., Geraldo Bastías, P., Jiang, S., Sun, Y. and Foster, J.G., 2024. A Primer on Deep Learning for Causal Inference. Sociological Methods & Research, p.00491241241234866.
• Read: Yao, L., Chu, Z., Li, S., Li, Y., Gao, J. and Zhang, A., 2021. A survey on causal inference. ACM Transactions on Knowledge Discovery from Data (TKDD), 15(5), pp.1-46.
• Read: Rubin, D. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association 100.469 (2005): 322-331.

Recommended Materials

• Athey, S, and Imbens, G. Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences 113, no. 27 (2016): 7353-7360.
• Wager, S., and Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523), 1228-1242.
• Suk, Y., Kang, H. and Kim, J.S., 2020. Random forests approach for causal inference with clustered observational data. Multivariate Behavioral Research, DOI: 10.1080/00273171.2020.1808437
• Hill, Jennifer L. Bayesian nonparametric modeling for causal inference. Journal of Computational and Graphical Statistics 20, no. 1 (2011): 217-240.
• Shalit, Uri, Fredrik D. Johansson, and David Sontag. Estimating individual treatment effect: generalization bounds and algorithms.. In International Conference on Machine Learning, pp. 3076-3085. PMLR, 2017.
• Yao, L., Li, S., Li, Y., Huai, M., Gao, J. and Zhang, A., 2018. Representation learning for treatment effect estimation from observational data. In Advances in Neural Information Processing Systems (pp. 2633-2643).
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J., 2018. Double/debiased machine learning for treatment and structural parameters". The Econometrics Journal, 21(1), pp.C1-C68.
• F. Johansson, U. Shalit, and D. Sontag. Learning representations for counterfactual inference. In International conference on machine learning (pp. 3020-3029).
• Yao, Liuyi, Sheng Li, Yaliang Li, Mengdi Huai, Jing Gao, and Aidong Zhang. Ace: Adaptively similarity-preserved representation learning for individual treatment effect estimation. In 2019 IEEE International Conference on Data Mining (ICDM), pp. 1432-1437. IEEE, 2019.
• Louizos, C., Shalit, U., Mooij, J.M., Sontag, D., Zemel, R. and Welling, M., 2017. Causal effect inference with deep latent-variable models. In Advances in Neural Information Processing Systems (pp. 6446-6456).
• Yoon, J., Jordon, J. and van der Schaar, M., 2018,GANITE: Estimation of individualized treatment effects using generative adversarial nets. In International Conference on Learning Representations. 2018.
• Jung, Yonghan, Jin Tian, and Elias Bareinboim. (2021). Estimating identifiable causal effects through double machine learning. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 13, pp. 12113-12122. 2021.
• Jung Y, Tian J, Bareinboim E. (2021). Estimating identifiable causal effects on markov equivalence class through double machine learning. In International Conference on Machine Learning. pp. 5168-5179. PMLR.
• Read: Goodfellow, I., Bengio, Y., Courville, A., & Bengio, Y. (2016), Deep learning (Chapter 14). Cambridge: MIT press.
• Doersch, C., 2016. Tutorial on variational autoencoders. arXiv preprint arXiv:1606.05908.

Causal effect estimation (continued). Natural experiments. Causal effect estimation using instrumental variables. Discontinuities as instrumental variables.

Basic approaches to learning causal graphs from data. Conditional independence based methods. Score based methods. Differentiable methods. Bayesian averaging based methods.

Required Materials

• Review: Honavar, V. Lecture Slides
• Heckerman, D., 1998, revised 2022. A tutorial on learning with Bayesian networks. Learning in graphical models, pp.301-354.
• Koski TJ, Noble J. (2012). A review of Bayesian networks and structure learning. Mathematica Applicanda. 40(1).
• Kitson, N.K., Constantinou, A.C., Guo, Z., Liu, Y. and Chobtham, K., 2023. A survey of Bayesian Network structure learning. Artificial Intelligence Review, 56(8), pp.8721-8814.
• Read: Glymour, Clark, Kun Zhang, and Peter Spirtes. Review of causal discovery methods based on graphical models. Frontiers in genetics 10 (2019): 524.
• Read: Drton, M. and Maathuis, M.H., 2017. Structure learning in graphical modeling. Annual Review of Statistics and Its Application, 4(1), pp.365-393.
• Vowels, Matthew J., Necati Cihan Camgoz, and Richard Bowden. D’ya like dags? a survey on structure learning and causal discovery. ACM Computing Surveys 55, no. 4 (2022): 1-36.

Recommended Materials

Craig, P., Katikireddi, S.V., Leyland, A. and Popham, F., 2017. Natural experiments: an overview of methods, approaches, and contributions to public health intervention research. Annual review of public health, 38, pp.39-56.
• Titiunik, R., 2020. Natural experiments. arXiv preprint arXiv:2002.00202.
• Hernán, M.A. and Robins, J.M., 2006. Instruments for causal inference: an epidemiologist's dream?. Epidemiology, pp.360-372.
• Swanson, S.A., Hernán, M.A., Miller, M., Robins, J.M. and Richardson, T.S., 2018. Partial identification of the average treatment effect using instrumental variables: review of methods for binary instruments, treatments, and outcomes. Journal of the American Statistical Association, 113(522), pp.933-947.
• Labrecque, Jeremy, and Sonja A. Swanson. Understanding the assumptions underlying instrumental variable analyses: a brief review of falsification strategies and related tools. Current epidemiology reports 5.3 (2018): 214-220.
• Malinsky, D. and Danks, D., 2018. Causal discovery algorithms: A practical guide. Philosophy Compass, 13(1), p.e12470.
• Scanagatta, M., Salmerón, A. and Stella, F., 2019. A survey on Bayesian network structure learning from data. Progress in Artificial Intelligence, 8(4), pp.425-439.
• Heinze-Deml, C., Maathuis, M.H. and Meinshausen, N., 2018. Causal structure learning. Annual Review of Statistics and Its Application, 5(1), pp.371-391.
• Li, F., Ding, P. and Mealli, F., 2023. Bayesian causal inference: a critical review. Philosophical Transactions of the Royal Society A, 381(2247), p.20220153.
• Scanagatta, M., de Campos, C.P., Corani, G. and Zaffalon, M., 2015. Learning Bayesian networks with thousands of variables. Advances in neural information processing systems, 28.
• Natori, K., Uto, M. and Ueno, M., 2017, September. Consistent learning Bayesian networks with thousands of variables. In Advanced Methodologies for Bayesian Networks (pp. 57-68). PMLR.
• Bromberg, F., Margaritis, D. and Honavar, V., 2009. Efficient Markov network structure discovery using independence tests. Journal of Artificial Intelligence Research, 35, pp.449-484.

Checking causal or identifiability assumptions; Bounds on Causal effects - no assumption bounds, Bounds on causal effects under monotone treatment response, monotone treatment selection, and optimal treatment selection assumptions.

Sensitivity analysis under the linear model and generalizations.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: Rubin, D. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association 100.469 (2005): 322-331.
• Read: Read: Neal, Brady (2020), Introduction to Causal Inference from a Machine Learning Perspective, Chapter 8.

Recommended Materials

• Manski, C.F., 1989. Anatomy of the selection problem. Journal of Human resources, pp.343-360.
• Manski, C.F., 1997. Monotone treatment response. Econometrica: Journal of the Econometric Society, pp.1311-1334.
• Manski, C.F. and Nagin, D.S., 1998. Bounding disagreements about treatment effects: A case study of sentencing and recidivism. Sociological methodology, 28(1), pp.99-137.
• Zhang, Junzhe, and Elias Bareinboim. Bounding causal effects on continuous outcome. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 13, pp. 12207-12215. 2021.
• Kilbertus, Niki, Matt J. Kusner, and Ricardo Silva. A class of algorithms for general instrumental variable models. Advances in Neural Information Processing Systems 33 (2020): 20108-20119.
• Ding, P. and VanderWeele, T.J., 2016. Sensitivity analysis without assumptions. Epidemiology (Cambridge, Mass.), 27(3), p.368.
• VanderWeele, T.J., 2010. Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology (Cambridge, Mass.), 21(4), p.540.

Causal transportability, multiple transportability, and related problems (meta analysis). Completeness of do-calculus for causal transportability and related problems.

Required Materials

• Review: Honavar, V. Lecture Slides
• Read: J. Pearl and E. Bareinboim, Transportability of Causal and Statistical Relations: A Formal Approach, 2011 IEEE 11th International Conference on Data Mining Workshops, Vancouver, BC, Canada, 2011, pp. 540-547, doi: 10.1109/ICDMW.2011.169.
• Degtiar, I. and Rose, S., 2023. A review of generalizability and transportability. Annual Review of Statistics and Its Application, 10, pp.501-524.

Recommended Materials

• Bareinboim, E., and Pearl, J. (2013). Meta-transportability of causal effects: A formal approach. In Artificial Intelligence and Statistics (pp. 135-143). PMLR.
• Lee, Sanghack, and Vasant Honavar. m-transportability: Transportability of a causal effect from multiple environments.Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 27. No. 1. 2013.
• Bareinboim, E., and Pearl, J. (2013). A general algorithm for deciding transportability of experimental results. Journal of causal Inference, 1(1), 107-134.
• Lee, Sanghack, and Vasant Honavar. Causal transportability of experiments on controllable subsets of variables: z-transportability. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, pp. 361-370. 2013.
• Bareinboim, Elias, and Judea Pearl. Causal transportability with limited experiments. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 27, no. 1, pp. 95-101. 2013.
• Bareinboim, Elias, Sanghack Lee, Vasant Honavar, and Judea Pearl. Transportability from multiple environments with limited experiments. Advances in Neural Information Processing Systems 26 (2013).
Bareinboim, E., and Pearl, J. (2016). Causal inference and the data-fusion problem. Proceedings of the National Academy of Sciences, 113(27), 7345-7352.
• Correa JD, Lee S, Bareinboim E. Counterfactual Transportability: A Formal Approach. InInternational Conference on Machine Learning 2022 (pp. 4370-4390). PMLR.

Relational Causal Models. Ground graphs and Abstract ground graphs. Relational d-separation. Characterization of the Equivalence Class of Relational Causal Models. Learning Relational Causal models from Relational Conditional Independence Queries. Relational Conditional Independence Tests. Learning relational causal models from data.

Required Materials

• Review: Honavar, V. Lecture Slides

Recommended Materials

• Maier, M., Taylor, B., Oktay, H. and Jensen, D., 2010, Learning causal models of relational domains. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 24, No. 1, pp. 531-538).
• Maier, Marc, Katerina Marazopoulou, David Arbour, and David Jensen. A sound and complete algorithm for learning causal models from relational data. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, pp. 371-380. 2013.
• Lee S, Honavar V. Lifted representation of relational causal models revisited: implications for reasoning and structure learning. In: Proceedings of the UAI 2015 Conference on Advances in Causal Inference-Volume 1504 2015 Jul 16 (pp. 56-65).
• Lee, Sanghack, and Vasant Honavar. A characterization of Markov equivalence classes of relational causal models under path semantics.In Proceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence, pp. 387-396. 2016.
• Lee S, Honavar V. On learning causal models from relational data. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence 2016 (pp. 3263-3270).
• Lee, Sanghack, and Vasant Honavar. A kernel conditional independence test for relational data. In 33rd Conference on Uncertainty in Artificial Intelligence, UAI 2017. 2017.
• Lee, S. and Honavar, V., 2020, Towards robust relational causal discovery. In Uncertainty in Artificial Intelligence (pp. 345-355). PMLR.
• Ahsan, Ragib, David Arbour, and Elena Zheleva. Relational Causal Models with Cycles: Representation and Reasoning. In Conference on Causal Learning and Reasoning, pp. 1-18. PMLR, 2022.
• Ahsan, R., Arbour, D., & Zheleva, E. (2022). Learning Relational Causal Models with Cycles through Relational Acyclification. arXiv preprint arXiv:2208.12210.