# Causal Discovery in the Presence of Missing Data

arXiv: https://arxiv.org/abs/1807.04010 · HTML: https://mlsanity.com/paper/1807.04010/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2018.

## Built on by (most cited first, 30 of 47)

- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Case Studies of Causal Discovery from IT Monitoring Time Series](https://mlsanity.com/paper/2307.15678/) (2023)
- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Causal Agent based on Large Language Model](https://mlsanity.com/paper/2408.06849/) (2024)
- [TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discovery](https://mlsanity.com/paper/2506.01361/) (2025)
- [The WHY in Business Processes: Discovery of Causal Execution Dependencies](https://mlsanity.com/paper/2310.14975/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Data](https://mlsanity.com/paper/2407.12254/) (2024)
- [On Testability and Goodness of Fit Tests in Missing Data Models](https://mlsanity.com/paper/2203.00132/) (2022)
- [A Review and Roadmap of Deep Learning Causal Discovery in Different Variable Paradigms](https://mlsanity.com/paper/2209.06367/) (2022)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Causally Constrained Data Synthesis for Private Data Release](https://mlsanity.com/paper/2105.13144/) (2021)
- [Deception by Omission: Using Adversarial Missingness to Poison Causal Structure Learning](https://mlsanity.com/paper/2305.20043/) (2023)
- [Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment Effect Estimation](https://mlsanity.com/paper/2307.04988/) (2023)
- [Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data](https://mlsanity.com/paper/2108.13331/) (2021)
- [Scalable Causal Structure Learning: Scoping Review of Traditional and Deep Learning Algorithms and New Opportunities in Biomedicine](https://mlsanity.com/paper/2110.07785/) (2021)

## 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.