Graphical Models

• Pearl, Judea. "Causal inference in statistics: An overview." Statistics surveys 3 (2009): 96-146. 

• Eberhardt, Frederick. "Introduction to the foundations of causal discovery." International Journal of Data Science and Analytics 3.2 (2017): 81-91. 

• Glymour, Clark, Kun Zhang, and Peter Spirtes. "Review of causal discovery methods based on graphical models." Frontiers in genetics 10 (2019): 524. 

• Drton, Mathias, and Marloes H. Maathuis. "Structure learning in graphical modeling." Annual Review of Statistics and Its Application 4 (2017): 365-393. 

• Uhler, Caroline, et al. "Geometry of the faithfulness assumption in causal inference." The Annals of Statistics (2013): 436-463. 

Constraint-based Algorithms

• Bühlmann, Peter, Markus Kalisch, and Lukas Meier. "High-dimensional statistics with a view toward applications in biology." Annual Review of Statistics and Its Application 1 (2014): 255-278. 

• Kalisch, Markus, and Peter Bühlman. "Estimating high-dimensional directed acyclic graphs with the PC-algorithm." Journal of Machine Learning Research 8.3 (2007). 

• Kalisch, Markus, and Peter Bühlmann. "Robustification of the PC-algorithm for directed acyclic graphs." Journal of Computational and Graphical Statistics 17.4 (2008): 773-789. 

• Bühlmann, Peter, Markus Kalisch, and Marloes H. Maathuis. "Variable selection in high-dimensional linear models: partially faithful distributions and the PC-simple algorithm." Biometrika 97.2 (2010): 261-278. 

• Harris, Naftali, and Mathias Drton. "PC algorithm for nonparanormal graphical models." Journal of Machine Learning Research 14.11 (2013).

• Le, Thuc Duy, et al. "A fast PC algorithm for high dimensional causal discovery with multi-core PCs." IEEE/ACM transactions on computational biology and bioinformatics 16.5 (2016): 1483-1495.

Score-based Algorithms

• Chickering, David Maxwell. "Optimal structure identification with greedy search." Journal of machine learning research 3.Nov (2002): 507-554. 

Hybrid Algorithms

• Tsamardinos, Ioannis, Laura E. Brown, and Constantin F. Aliferis. "The max-min hill-climbing Bayesian network structure learning algorithm." Machine learning 65.1 (2006): 31-78. 

Non-Gaussian DAG Models

• Shimizu, Shohei, et al. "A linear non-Gaussian acyclic model for causal discovery." Journal of Machine Learning Research 7.10 (2006). 

• Inazumi, Takanori, Shohei Shimizu, and Takashi Washio. "Use of prior knowledge in a non-Gaussian method for learning linear structural equation models." International Conference on Latent Variable Analysis and Signal Separation. Springer, Berlin, Heidelberg, 2010. 

• Shimizu, Shohei, et al. "DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model." The Journal of Machine Learning Research 12 (2011): 1225-1248. 

• Shimizu, Shohei, et al. "Discovery of non-gaussian linear causal models using ICA." arXiv preprint arXiv:1207.1413 (2012). 

• Shimizu, Shohei, Aapo Hyvarinen, and Yoshinobu Kawahara. "A direct method for estimating a causal ordering in a linear non-gaussian acyclic model." arXiv preprint arXiv:1408.2038 (2014). 

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• Hyvarinen, Aapo. "Pairwise measures of causal direction in linear non-gaussian acyclic models." Proceedings of 2nd Asian Conference on Machine Learning. JMLR Workshop and Conference Proceedings, 2010. 

• Feng, Dingcheng, Feng Chen, and Wenli Xu. "Learning linear non-Gaussian networks: A new view from matrix identification." Journal of Experimental & Theoretical Artificial Intelligence 25.2 (2013): 251-271. 

• Wiedermann, Wolfgang. "Decisions concerning the direction of effects in linear regression models using fourth central moments." Dependent data in social sciences research. Springer, Cham, 2015. 149-169. 

• Cai, Ruichu, et al. "An efficient kurtosis-based causal discovery method for linear non-Gaussian acyclic data." 2017 IEEE/ACM 25th International Symposium on Quality of Service (IWQoS). IEEE, 2017. 

• Hyvärinen, Aapo, and Stephen M. Smith. "Pairwise likelihood ratios for estimation of non-Gaussian structural equation models." Journal of Machine Learning Research 14.Jan (2013): 111-152. 

• Wang, Y. Samuel, and Mathias Drton. "High-dimensional causal discovery under non-Gaussianity." Biometrika 107.1 (2020): 41-59. 

• Mai, Guizhen, et al. "Distinguish Markov Equivalence Classes from Large-Scale Linear Non-Gaussian Data." IEEE Access 8 (2020): 10924-10932. 

• Améndola, Carlos, et al. "Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models." arXiv preprint arXiv:2112.10875 (2021). 

• Harada, Kazuharu, and Hironori Fujisawa. "Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery." Neurocomputing 459 (2021): 223-233. 

• Shahbazinia, Amirhossein, Saber Salehkaleybar, and Matin Hashemi. "ParaLiNGAM: Parallel Causal Structure Learning for Linear non-Gaussian Acyclic Models." arXiv preprint arXiv:2109.13993 (2021). 

• Zhao, Ruixuan, Xin He, and Junhui Wang. "Learning linear non-Gaussian directed acyclic graph with diverging number of nodes." arXiv preprint arXiv:2111.00740 (2021). 

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Linear SEM

• Foygel, Rina, Jan Draisma, and Mathias Drton. "Half-trek criterion for generic identifiability of linear structural equation models." The Annals of Statistics (2012): 1682-1713. 

• Peters, Jonas, and Peter Bühlmann. "Identifiability of Gaussian structural equation models with equal error variances." Biometrika 101.1 (2014): 219-228. 

• Loh, Po-Ling, and Peter Bühlmann. "High-dimensional learning of linear causal networks via inverse covariance estimation." The Journal of Machine Learning Research 15.1 (2014): 3065-3105. 

• Wiedermann, Wolfgang, Michael Hagmann, and Alexander von Eye. "Significance tests to determine the direction of effects in linear regression models." British Journal of Mathematical and Statistical Psychology 68.1 (2015): 116-141. 

• Ghoshal, Asish, and Jean Honorio. "Learning identifiable gaussian bayesian networks in polynomial time and sample complexity." Advances in Neural Information Processing Systems 30 (2017). 

• Ghoshal, Asish, and Jean Honorio. "Learning linear structural equation models in polynomial time and sample complexity." International Conference on Artificial Intelligence and Statistics. PMLR, 2018. 

• Park, Gunwoong, and Yesool Kim. "Learning high-dimensional gaussian linear structural equation models with heterogeneous error variances." Computational Statistics & Data Analysis 154 (2021): 107084. 

• Park, Sion, and Gunwoong Park. "Robust estimation of Gaussian linear structural equation models with equal error variances." Journal of the Korean Statistical Society (2022): 1-22. 

Non-linear ANM

General ANM

Count DAG Models

• Fang, Zhuangyan, et al. "Low Rank Directed Acyclic Graphs and Causal Structure Learning." arXiv preprint arXiv:2006.05691 (2020). 

• Yu, Shiqing, Mathias Drton, and Ali Shojaie. "Directed graphical models and causal discovery for zero-inflated data." arXiv preprint arXiv:2004.04150 (2020). 

• Park, Gunwoong, et al. "Learning a high-dimensional linear structural equation model via l1-regularized regression." Journal of Machine Learning Research 22.102 (2021): 1-41. 

Others

• Entner, Doris, and Patrik O. Hoyer. "Estimating a causal order among groups of variables in linear models." International Conference on Artificial Neural Networks. Springer, Berlin, Heidelberg, 2012. 

• Wiedermann, Wolfgang, and Alexander von Eye. "Direction of effects in mediation analysis." Psychological Methods 20.2 (2015): 221. 

• Wiedermann, Wolfgang, and Alexander von Eye. "Direction of effects in multiple linear regression models." Multivariate Behavioral Research 50.1 (2015): 23-40. 

• Sokol, Alexander, Marloes H. Maathuis, and Benjamin Falkeborg. "Quantifying identifiability in independent component analysis." Electronic Journal of Statistics 8.1 (2014): 1438-1459.

• Hoyer, Patrik O., et al. "Causal discovery of linear acyclic models with arbitrary distributions." arXiv preprint arXiv:1206.3260 (2012). 

• Wiedermann, Wolfgang, and Michael Hagmann. "Asymmetric properties of the Pearson correlation coefficient: Correlation as the negative association between linear regression residuals." Communications in Statistics-Theory and Methods 45.21 (2016): 6263-6283. 

• Gnecco, Nicola, et al. "Causal discovery in heavy-tailed models." The Annals of Statistics 49.3 (2021): 1755-1778. 

• Dodge, Yadolah, and Valentin Rousson. "On asymmetric properties of the correlation coeffcient in the regression setting." The American Statistician 55.1 (2001): 51-54. 

• Dodge, Yadolah, and Valentin Rousson. "Direction dependence in a regression line." Communications in Statistics-Theory and Methods 29.9-10 (2000): 1957-1972. 

• Harada, Kazuharu, and Hironori Fujisawa. "Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis." arXiv preprint arXiv:2009.03077 (2020). 

• Ng, Ignavier, AmirEmad Ghassami, and Kun Zhang. "On the role of sparsity and dag constraints for learning linear dags." Advances in Neural Information Processing Systems 33 (2020): 17943-17954. 

• Zhang, Hao, et al. "Learning causal structures based on divide and conquer." IEEE Transactions on Cybernetics (2020). 

• Kaiser, Marcus, and Maksim Sipos. "Unsuitability of NOTEARS for Causal Graph Discovery." arXiv preprint arXiv:2104.05441 (2021). 

• Zheng, Xun, et al. "Dags with no tears: Continuous optimization for structure learning." Advances in Neural Information Processing Systems 31 (2018). 

• Hoyer, Patrik O., and Antti Hyttinen. "Bayesian discovery of linear acyclic causal models." arXiv preprint arXiv:1205.2641 (2012).