Current status and application examples of causal discovery methods based on observational data_Chinese Journal of Evidence-Based Medicine

Authors：

LIU Zuting , CHEN Wenjuan , YANG Xia , LUO Tian , MA Hailin , ZHANG Huiqin , LE Shixin , ZHOU Ting , WANG Haojie ,  KUANG Jie

School of Public Health, Jiangxi Medical College, Nanchang University, Jiangxi Provincial Key Laboratory of Disease Prevention and Public Health, Nanchang 330006, P. R. China;

Corresponding author：

KUANG Jie, Email: kuangjie@ncu.edu.cn

Keywords：

Causal discovery; Observational data; Causal effect; R language

DOI：

10.7507/1672-2531.202504070

Video：

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Machine learning methods typically focus on the correlations within data while neglecting the causal relationships that reveal underlying mechanisms. This limitation may restrict the reliability and interpretability of models in decision support and intervention strategies. For this reason, causal discovery methods have gained widespread attention. They can infer causal structures and directions between variables from observational data, thereby providing decision-makers with an interpretable and intervenable analytical framework. This review introduces commonly used causal discovery methods based on observational data. Combined with specific case studies, it demonstrates and practices these methods using the R language, aiming to provide readers with practical references for understanding and applying causal discovery methods.

1.	Pearl J. Causality: models, reasoning and inference. Cambridge: Cambridge University Press, 2009.
2.	Spirtes P, Glymour C, Scheines R. Causation, prediction, and search. Cambridge: MIT Press, 2001.
3.	Angrist JD, Pischke JS. Mostly harmless econometrics: an empiricist's companion. Princeton: Princeton University Press, 2009.
4.	Vowels MJ, Camgoz NC, Bowden R. D’ya like dags. a survey on structure learning and causal discovery. ACM Comput Surv, 2022, 55(4): 1-36.
5.	Peters J, Janzing D, Schölkopf B. Elements of causal inference: foundations and learning algorithms. Cambridge: MIT Press, 2017.
6.	Deaton A, Cartwright N. Understanding and misunderstanding randomized controlled trials. Soc Sci Med, 2018, 210: 2-21.
7.	Pearl J, Mackenzie D. The book of why: the new science of cause and effect. New York: Basic Books, 2018.
8.	Verma T, Pearl J. Equivalence and synthesis of causal models. Cambridge: Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence, 1990.
9.	Park K, Waldorp LJ, Ryan O. Discovering cyclic causal models in psychological research. Adv Psychol, 2024, 2: e72425.
10.	Colombo D, Maathuis MH, Kalisch M, et al. Learning high-dimensional directed acyclic graphs with latent and selection variables. Ann Stat, 2012, 40(1): 294-321.
11.	Kummerfeld E, Ramsey J, Yang R, et al. Causal clustering for 2-factor measurement models. Heidelberg: Proceedings of the 2014th European Conference on Machine Learning and Knowledge Discovery in Databases, 2014: 34-49.
12.	Strobl EV. A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias. J Data Sci Anal, 2019, 8(1): 33-56.
13.	Ribeiro AH, Crnkovic M, Pereira JL, et al. AnchorFCI: harnessing genetic anchors for enhanced causal discovery of cardiometabolic disease pathways. Front Genet, 2024, 15: 1436947.
14.	Sutton RS, Barto AG. Reinforcement learning: an introduction. Cambridge: MIT press, 1998.
15.	Chickering DM. Optimal structure identification with greedy search. JMLR, 2002, 3: 507-554.
16.	Ramsey J, Glymour M, Sanchez-Romero R, et al. A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images. Int J Data Sci Anal, 2017, 3(2): 121-129.
17.	Rathnam C, Lee S, Jiang X. An algorithm for direct causal learning of influences on patient outcomes. Artif Intell Med, 2017, 75: 1-15.
18.	Icasia G, Tyasnurita R, Purba E. Application of heuristic combinations within a hyper-heuristic framework for exam scheduling problems. RESTI, 2020, 4: 664-671.
19.	Ni Y. Bivariate causal discovery for categorical data via classification with optimal label permutation. Adv Neural Inf Process Syst, 2022, 35: 10837-10848.
20.	Wang M, Shen X, Pan W. Causal discovery with generalized linear models through peeling algorithms. J Mach Learn Res, 2024, 25: 310.
21.	Tsamardinos I, Brown LE, Aliferis CF. The max-min hill-climbing Bayesian network structure learning algorithm. Mach Learn, 2006, 65(1): 31-78.
22.	Badsha MB, Martin EA, Fu AQ. MRPC: an R package for inference of causal graphs. Front Genet, 2021, 12: 651812.
23.	Shimizu S, Hoyer PO, Hyvärinen A, et al. ^{A linear non-Gaussian acyclic model for causal} discovery. J Mach Learn Res, 2006, 7: 2003-2030.
24.	Chen W, Cai R, Zhang K, et al. Causal discovery in linear non-gaussian acyclic model with multiple latent confounders. IEEE Trans Neural Netw Learn Syst, 2022, 33(7): 2816-2827.
25.	Shimizu S, Inazumi T, Sogawa Y, et al. DirectLiNGAM: a direct method for learning a linear non-Gaussian structural equation model. J Mach Learn Res, 2011, 12: 1225-1248.
26.	Chen Z, Chan L. Causality in linear nongaussian acyclic models in the presence of latent gaussian confounders. Neural Comput, 2013, 25(6): 1605-1641.
27.	Yamayoshi M, Tsuchida J, Yadohisa H. An estimation of causal structure based on Latent LiNGAM for mixed data. Behaviormetrika, 2020, 47(1): 105-121.
28.	Zhang K, Hyvärinen A. On the identifiability of the post-nonlinear causal model. Arlington: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, 2009: 647-655.
29.	Peters J, Janzing D, Schölkopf B. Causal inference on discrete data using additive noise models. IEEE Trans Pattern Anal Mach Intell, 2011, 33(12): 2436-2450.
30.	Zhang K, Schölkopf B, Janzing D. Invariant Gaussian process latent variable models and application in causal discovery. Arlington: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, 2010: 717-724.
31.	Janzing D, Mooij J, Zhang K, et al. Information-geometric approach to inferring causal directions. Artif Intell, 2012, 182-183: 1-31.
32.	Bühlmann P, Peters J, Ernest J. CAM: causal additive models, high-dimensional order search and penalized regression. Ann Stat, 2013, 42(6): 2526-2556.
33.	Peters J, Mooij JM, Janzing D, et al. Causal discovery with continuous additive noise models. J Mach Learn Res, 2014, 15(1): 2009-2053.
34.	Hu S, Chen Z, Chan L. A kernel embedding-based approach for nonstationary causal model inference. Neural Comput, 2018, 30(5): 1394-1425.
35.	Zeng Y, Hao Z, Cai R, et al. A causal discovery algorithm based on the prior selection of leaf nodes. Neural Netw, 2020, 124: 130-145.
36.	Xie F, Cai R, Zeng Y, et al. An efficient entropy-based causal discovery method for linear structural equation models with IID noise variables. IEEE Trans Neural Netw Learn Syst, 2020, 31(5): 1667-1680.
37.	Yu S, Drton M, Shojaie A. Directed graphical models and causal discovery for zero-inflated data. Proc Mach Learn Res, 2023, 213: 27-67.
38.	Rogovchenko V, Sibu A, Ni Y. Scalar-function causal discovery for generating causal hypotheses with observational wearable device data. Pac Symp Biocomput, 2024, 29: 201-213.
39.	Arda E, Küçükkocaoğlu G. Stock price predictions using artificial intelligence methods. EPFAD, 2021, 6(2): 565-586.
40.	Zheng X, Aragam B, Ravikumar P, et al. DAGs with NO TEARS: continuous optimization for structure learning. NeurIPS, 2018.
41.	Lundberg SM, Lee SI. A unified approach to interpreting model predictions. New York: Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017: 4768-4777.
42.	Peters J, Buhlmann P, Meinshausen N. Causal inference by using invariant prediction: identification and confidence intervals. J R Stat Soc Ser B, 2016, (5): 947-1012.
43.	LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444.
44.	Heaton J. Ian Goodfellow, Yoshua Bengio, and Aaron Courville: deep learning. Genet Program Evol Mach, 2018, 19(1): 305-307.
45.	Petersen AH, Ramsey J, Ekstrøm CT, et al. Causal discovery for observational sciences using supervised machine learning. J Data Sci, 2023, 21(2): 255-280.
46.	Henao R, Winther O. Sparse linear identifiable multivariate modeling. J Mach Learn Res, 2011, 12(3): 863-905.
47.	Chaves R, Luft L, Maciel TO, et al. Inferring latent structures via information inequalities. Arlington: Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, 2014: 112-121.
48.	Hill SM, Oates CJ, Blythe DA, et al. Causal learning via manifold regularization. J Mach Learn Res, 2019, 20(127): 1-32.
49.	Yu Y, Chen J, Gao T, et al. DAG-GNN: DAG structure learning with graph neural networks. Cambridge: Proceedings of the 36 th International Conference on Machine Learning, 2019.
50.	Ge X, Raghu VK, Chrysanthis PK, et al. CausalMGM: an interactive web-based causal discovery tool. Nucleic Acids Res, 2020, 48(W1): W597-W602.
51.	Kalainathan D, Goudet O, Guyon I, et al. Structural agnostic modeling: adversarial learning of causal graphs. J Mach Learn Res, 2022, 23(219): 1-62.
52.	Zhou F, He K, Ni Y. Individualized causal discovery with latent trajectory embedded Bayesian networks. Biometrics, 2023, 79(4): 3191-3202.
53.	Roy S, Wong RKW, Ni Y. Directed cyclic graph for causal discovery from multivariate functional data. Adv Neural Inf Process Syst, 2023, 36: 42762-42774.
54.	Li C, Shen X, Pan W. Nonlinear causal discovery with confounders. J Am Stat Assoc, 2024, 119(546): 1205-1214.
55.	Wei Y, Li X, Lin L, et al. Causal discovery on discrete data via weighted normalized wasserstein distance. IEEE Trans Neural Netw Learn Syst, 2024, 35(4): 4911-4923.
56.	Dang Y, Gao X, Wang Z. A novel hyper-heuristic algorithm with soft and hard constraints for causal discovery using a linear structural equation model. Entropy (Basel), 2025, 27(1): 38.
57.	Chernozhukov V, Chetverikov D, Demirer M, et al. Double/debiased machine learning for treatment and structural parameters. Econom J, 2018, 21(1): C1-C68.
58.	Scutari M. Learning Bayesian networks with the bnlearn R package. J Stat Softw, 2010, 35(3): 1-22.
59.	Kalisch M, Mächler M, Colombo D, et al. Causal inference using graphical models with the R package pcalg. J Stat Softw, 2012, 47(11): 1-26.
60.	Andrews RM, Bang CW, Didelez V, et al. Software application profile: tpc and micd-R packages for causal discovery with incomplete cohort data. Int J Epidemiol, 2024, 53(5): dyae113.
61.	Le TD, Xu T, Liu L, et al. ParallelPC: an R package for efficient causal exploration in genomic data. Proceedings of the Trends and Applications in Knowledge Discovery and Data Mining: PAKDD 2018 Workshops, 2018.
62.	Liu Y. CWGCNA: an R package to perform causal inference from the WGCNA framework. NAR Genom Bioinform, 2024, 6(2): lqae042.
63.	Zhang J, Kummerfield E, Hultman G, et al. Application of causal discovery algorithms in studying the nephrotoxicity of remdesivir using longitudinal data from the EHR. AMIA Annu Symp Proc, 2023, 2022: 1227-1236.
64.	Sokolova E, von Rhein D, Naaijen J, et al. Handling hybrid and missing data in constraint-based causal discovery to study the etiology of ADHD. Int J Data Sci Anal, 2017, 3(2): 105-119.
65.	Wen Y, Huang J, Guo S, et al. Applying causal discovery to single-cell analyses using CausalCell. Elife, 2023, 12: e81464.

1. Pearl J. Causality: models, reasoning and inference. Cambridge: Cambridge University Press, 2009.
2. Spirtes P, Glymour C, Scheines R. Causation, prediction, and search. Cambridge: MIT Press, 2001.
3. Angrist JD, Pischke JS. Mostly harmless econometrics: an empiricist's companion. Princeton: Princeton University Press, 2009.
4. Vowels MJ, Camgoz NC, Bowden R. D’ya like dags. a survey on structure learning and causal discovery. ACM Comput Surv, 2022, 55(4): 1-36.
5. Peters J, Janzing D, Schölkopf B. Elements of causal inference: foundations and learning algorithms. Cambridge: MIT Press, 2017.
6. Deaton A, Cartwright N. Understanding and misunderstanding randomized controlled trials. Soc Sci Med, 2018, 210: 2-21.
7. Pearl J, Mackenzie D. The book of why: the new science of cause and effect. New York: Basic Books, 2018.
8. Verma T, Pearl J. Equivalence and synthesis of causal models. Cambridge: Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence, 1990.
9. Park K, Waldorp LJ, Ryan O. Discovering cyclic causal models in psychological research. Adv Psychol, 2024, 2: e72425.
10. Colombo D, Maathuis MH, Kalisch M, et al. Learning high-dimensional directed acyclic graphs with latent and selection variables. Ann Stat, 2012, 40(1): 294-321.
11. Kummerfeld E, Ramsey J, Yang R, et al. Causal clustering for 2-factor measurement models. Heidelberg: Proceedings of the 2014th European Conference on Machine Learning and Knowledge Discovery in Databases, 2014: 34-49.
12. Strobl EV. A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias. J Data Sci Anal, 2019, 8(1): 33-56.
13. Ribeiro AH, Crnkovic M, Pereira JL, et al. AnchorFCI: harnessing genetic anchors for enhanced causal discovery of cardiometabolic disease pathways. Front Genet, 2024, 15: 1436947.
14. Sutton RS, Barto AG. Reinforcement learning: an introduction. Cambridge: MIT press, 1998.
15. Chickering DM. Optimal structure identification with greedy search. JMLR, 2002, 3: 507-554.
16. Ramsey J, Glymour M, Sanchez-Romero R, et al. A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images. Int J Data Sci Anal, 2017, 3(2): 121-129.
17. Rathnam C, Lee S, Jiang X. An algorithm for direct causal learning of influences on patient outcomes. Artif Intell Med, 2017, 75: 1-15.
18. Icasia G, Tyasnurita R, Purba E. Application of heuristic combinations within a hyper-heuristic framework for exam scheduling problems. RESTI, 2020, 4: 664-671.
19. Ni Y. Bivariate causal discovery for categorical data via classification with optimal label permutation. Adv Neural Inf Process Syst, 2022, 35: 10837-10848.
20. Wang M, Shen X, Pan W. Causal discovery with generalized linear models through peeling algorithms. J Mach Learn Res, 2024, 25: 310.
21. Tsamardinos I, Brown LE, Aliferis CF. The max-min hill-climbing Bayesian network structure learning algorithm. Mach Learn, 2006, 65(1): 31-78.
22. Badsha MB, Martin EA, Fu AQ. MRPC: an R package for inference of causal graphs. Front Genet, 2021, 12: 651812.
23. Shimizu S, Hoyer PO, Hyvärinen A, et al. ^{A linear non-Gaussian acyclic model for causal} discovery. J Mach Learn Res, 2006, 7: 2003-2030.
24. Chen W, Cai R, Zhang K, et al. Causal discovery in linear non-gaussian acyclic model with multiple latent confounders. IEEE Trans Neural Netw Learn Syst, 2022, 33(7): 2816-2827.
25. Shimizu S, Inazumi T, Sogawa Y, et al. DirectLiNGAM: a direct method for learning a linear non-Gaussian structural equation model. J Mach Learn Res, 2011, 12: 1225-1248.
26. Chen Z, Chan L. Causality in linear nongaussian acyclic models in the presence of latent gaussian confounders. Neural Comput, 2013, 25(6): 1605-1641.
27. Yamayoshi M, Tsuchida J, Yadohisa H. An estimation of causal structure based on Latent LiNGAM for mixed data. Behaviormetrika, 2020, 47(1): 105-121.
28. Zhang K, Hyvärinen A. On the identifiability of the post-nonlinear causal model. Arlington: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, 2009: 647-655.
29. Peters J, Janzing D, Schölkopf B. Causal inference on discrete data using additive noise models. IEEE Trans Pattern Anal Mach Intell, 2011, 33(12): 2436-2450.
30. Zhang K, Schölkopf B, Janzing D. Invariant Gaussian process latent variable models and application in causal discovery. Arlington: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, 2010: 717-724.
31. Janzing D, Mooij J, Zhang K, et al. Information-geometric approach to inferring causal directions. Artif Intell, 2012, 182-183: 1-31.
32. Bühlmann P, Peters J, Ernest J. CAM: causal additive models, high-dimensional order search and penalized regression. Ann Stat, 2013, 42(6): 2526-2556.
33. Peters J, Mooij JM, Janzing D, et al. Causal discovery with continuous additive noise models. J Mach Learn Res, 2014, 15(1): 2009-2053.
34. Hu S, Chen Z, Chan L. A kernel embedding-based approach for nonstationary causal model inference. Neural Comput, 2018, 30(5): 1394-1425.
35. Zeng Y, Hao Z, Cai R, et al. A causal discovery algorithm based on the prior selection of leaf nodes. Neural Netw, 2020, 124: 130-145.
36. Xie F, Cai R, Zeng Y, et al. An efficient entropy-based causal discovery method for linear structural equation models with IID noise variables. IEEE Trans Neural Netw Learn Syst, 2020, 31(5): 1667-1680.
37. Yu S, Drton M, Shojaie A. Directed graphical models and causal discovery for zero-inflated data. Proc Mach Learn Res, 2023, 213: 27-67.
38. Rogovchenko V, Sibu A, Ni Y. Scalar-function causal discovery for generating causal hypotheses with observational wearable device data. Pac Symp Biocomput, 2024, 29: 201-213.
39. Arda E, Küçükkocaoğlu G. Stock price predictions using artificial intelligence methods. EPFAD, 2021, 6(2): 565-586.
40. Zheng X, Aragam B, Ravikumar P, et al. DAGs with NO TEARS: continuous optimization for structure learning. NeurIPS, 2018.
41. Lundberg SM, Lee SI. A unified approach to interpreting model predictions. New York: Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017: 4768-4777.
42. Peters J, Buhlmann P, Meinshausen N. Causal inference by using invariant prediction: identification and confidence intervals. J R Stat Soc Ser B, 2016, (5): 947-1012.
43. LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444.
44. Heaton J. Ian Goodfellow, Yoshua Bengio, and Aaron Courville: deep learning. Genet Program Evol Mach, 2018, 19(1): 305-307.
45. Petersen AH, Ramsey J, Ekstrøm CT, et al. Causal discovery for observational sciences using supervised machine learning. J Data Sci, 2023, 21(2): 255-280.
46. Henao R, Winther O. Sparse linear identifiable multivariate modeling. J Mach Learn Res, 2011, 12(3): 863-905.
47. Chaves R, Luft L, Maciel TO, et al. Inferring latent structures via information inequalities. Arlington: Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, 2014: 112-121.
48. Hill SM, Oates CJ, Blythe DA, et al. Causal learning via manifold regularization. J Mach Learn Res, 2019, 20(127): 1-32.
49. Yu Y, Chen J, Gao T, et al. DAG-GNN: DAG structure learning with graph neural networks. Cambridge: Proceedings of the 36 th International Conference on Machine Learning, 2019.
50. Ge X, Raghu VK, Chrysanthis PK, et al. CausalMGM: an interactive web-based causal discovery tool. Nucleic Acids Res, 2020, 48(W1): W597-W602.
51. Kalainathan D, Goudet O, Guyon I, et al. Structural agnostic modeling: adversarial learning of causal graphs. J Mach Learn Res, 2022, 23(219): 1-62.
52. Zhou F, He K, Ni Y. Individualized causal discovery with latent trajectory embedded Bayesian networks. Biometrics, 2023, 79(4): 3191-3202.
53. Roy S, Wong RKW, Ni Y. Directed cyclic graph for causal discovery from multivariate functional data. Adv Neural Inf Process Syst, 2023, 36: 42762-42774.
54. Li C, Shen X, Pan W. Nonlinear causal discovery with confounders. J Am Stat Assoc, 2024, 119(546): 1205-1214.
55. Wei Y, Li X, Lin L, et al. Causal discovery on discrete data via weighted normalized wasserstein distance. IEEE Trans Neural Netw Learn Syst, 2024, 35(4): 4911-4923.
56. Dang Y, Gao X, Wang Z. A novel hyper-heuristic algorithm with soft and hard constraints for causal discovery using a linear structural equation model. Entropy (Basel), 2025, 27(1): 38.
57. Chernozhukov V, Chetverikov D, Demirer M, et al. Double/debiased machine learning for treatment and structural parameters. Econom J, 2018, 21(1): C1-C68.
58. Scutari M. Learning Bayesian networks with the bnlearn R package. J Stat Softw, 2010, 35(3): 1-22.
59. Kalisch M, Mächler M, Colombo D, et al. Causal inference using graphical models with the R package pcalg. J Stat Softw, 2012, 47(11): 1-26.
60. Andrews RM, Bang CW, Didelez V, et al. Software application profile: tpc and micd-R packages for causal discovery with incomplete cohort data. Int J Epidemiol, 2024, 53(5): dyae113.
61. Le TD, Xu T, Liu L, et al. ParallelPC: an R package for efficient causal exploration in genomic data. Proceedings of the Trends and Applications in Knowledge Discovery and Data Mining: PAKDD 2018 Workshops, 2018.
62. Liu Y. CWGCNA: an R package to perform causal inference from the WGCNA framework. NAR Genom Bioinform, 2024, 6(2): lqae042.
63. Zhang J, Kummerfield E, Hultman G, et al. Application of causal discovery algorithms in studying the nephrotoxicity of remdesivir using longitudinal data from the EHR. AMIA Annu Symp Proc, 2023, 2022: 1227-1236.
64. Sokolova E, von Rhein D, Naaijen J, et al. Handling hybrid and missing data in constraint-based causal discovery to study the etiology of ADHD. Int J Data Sci Anal, 2017, 3(2): 105-119.
65. Wen Y, Huang J, Guo S, et al. Applying causal discovery to single-cell analyses using CausalCell. Elife, 2023, 12: e81464.

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