mlsanityData to 7 Oct 2026

Causal Discovery in the Presence of Missing Data

arXiv 1807.04010 ↗First posted 11 Jul 2018cs.LG stat.MLcited by 46

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Abstract (arXiv)

Missing data are ubiquitous in many domains including healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that follow different missingness mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs, we analyse conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose the Missing Value PC (MVPC) algorithm for both continuous and binary variables, which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on synthetic data show that the proposed algorithm is able to find correct causal relations even in the general case of MNAR. Moreover, we create a neuropathic pain diagnostic simulator for evaluating causal discovery methods. Evaluated on such simulated neuropathic pain diagnosis records and the other two real world applications, MVPC outperforms the other benchmark methods.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jul 2018.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 11; 2024: 8; 2025: 7; 2026: 4.

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  1. 2023Causal-learn: Causal Discovery in Pythoncited by 108
  2. 2022Deep End-to-end Causal Inferencecited by 93
  3. 2021A survey of Bayesian Network structure learningcited by 85
  4. 2021MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanismscited by 50
  5. 2023Discovering Causal Relations and Equations from Datacited by 33
  6. 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 32
  7. 2021Identifiable Generative Models for Missing Not at Random Data Imputationcited by 30
  8. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  9. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16
  10. 2022Local Constraint-Based Causal Discovery under Selection Biascited by 15
  11. 2023Case Studies of Causal Discovery from IT Monitoring Time Seriescited by 14
  12. 2021Greedy structure learning from data that contain systematic missing valuescited by 12
34 more
  1. 2021Causal Discovery from Conditionally Stationary Time Seriescited by 11
  2. 2024Gene Regulatory Network Inference in the Presence of Dropouts: a Causal Viewcited by 11
  3. 2021Clustering and Structural Robustness in Causal Diagramscited by 10
  4. 2024Causal Agent based on Large Language Modelcited by 10
  5. 2025TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discoverycited by 9
  6. 2023The WHY in Business Processes: Discovery of Causal Execution Dependenciescited by 7
  7. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  8. 2024COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Datacited by 5
  9. 2022On Testability and Goodness of Fit Tests in Missing Data Modelscited by 4
  10. 2022A Review and Roadmap of Deep Learning Causal Discovery in Different Variable Paradigmscited by 4
  11. 2023Robust Causal Bandits for Linear Modelscited by 4
  12. 2025The Robustness of Differentiable Causal Discovery in Misspecified Scenarioscited by 4
  13. 2021Causally Constrained Data Synthesis for Private Data Releasecited by 3
  14. 2023Deception by Omission: Using Adversarial Missingness to Poison Causal Structure Learningcited by 3
  15. 2023Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment Effect Estimationcited by 3
  16. 2023Identification of Causal Structure in the Presence of Missing Data with Additive Noise Modelcited by 3
  17. 2021Multiple imputation and test-wise deletion for causal discovery with incomplete cohort datacited by 2
  18. 2021Scalable Causal Structure Learning: Scoping Review of Traditional and Deep Learning Algorithms and New Opportunities in Biomedicinecited by 2
  19. 2024Improved Bound for Robust Causal Bandits with Linear Modelscited by 2
  20. 2025Causal Discovery on Higher-Order Interactionscited by 2
  21. 2022GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studiescited by 1
  22. 2023A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representationscited by 1
  23. 2024Learning Cyclic Causal Models from Incomplete Datacited by 1
  24. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  25. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  26. 2025Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Supportcited by 1
  27. 2023Towards a Transportable Causal Network Model Based on Observational Healthcare Datacited by 0
  28. 2024ION-C: Integration of Overlapping Networks via Constraintscited by 0
  29. 2025Learning Over Dirty Data with Minimal Repairscited by 0
  30. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0
  31. 2026PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Datacited by 0
  32. 2026Causal Modeling of Selection in Evolutioncited by 0
  33. 2026Causal Discovery in the Era of Agentscited by 0
  34. 2026GoT-CD: Graph-of-Thoughts Causal Discovery and the Fragility of Post-hoc Path-Specific Fairness Auditscited by 0