mlsanityData to 7 Oct 2026

MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models

arXiv 2205.13869 ↗First posted 27 May 2022cs.LG stat.MLcited by 21

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Abstract (arXiv)

State-of-the-art causal discovery methods usually assume that the observational data is complete. However, the missing data problem is pervasive in many practical scenarios such as clinical trials, economics, and biology. One straightforward way to address the missing data problem is first to impute the data using off-the-shelf imputation methods and then apply existing causal discovery methods. However, such a two-step method may suffer from suboptimality, as the imputation algorithm may introduce bias for modeling the underlying data distribution. In this paper, we develop a general method, which we call MissDAG, to perform causal discovery from data with incomplete observations. Focusing mainly on the assumptions of ignorable missingness and the identifiable additive noise models (ANMs), MissDAG maximizes the expected likelihood of the visible part of observations under the expectation-maximization (EM) framework. In the E-step, in cases where computing the posterior distributions of parameters in closed-form is not feasible, Monte Carlo EM is leveraged to approximate the likelihood. In the M-step, MissDAG leverages the density transformation to model the noise distributions with simpler and specific formulations by virtue of the ANMs and uses a likelihood-based causal discovery algorithm with directed acyclic graph constraint. We demonstrate the flexibility of MissDAG for incorporating various causal discovery algorithms and its efficacy through extensive simulations and real data experiments.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 28 of its 88 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

28 of 88 references.

References · 28

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 349
  3. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  4. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  5. 2019Gradient-Based Neural DAG Learningcited by 227
  6. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  7. 2019Learning Sparse Nonparametric DAGscited by 207
  8. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  9. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  10. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  11. 2019Causal Discovery with Reinforcement Learningcited by 145
  12. 2020Missing Data Imputation using Optimal Transportcited by 99
16 more
  1. 2022Deep End-to-end Causal Inferencecited by 93
  2. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  3. 2018Graphical Models for Processing Missing Datacited by 57
  4. 2020A Tutorial on Learning With Bayesian Networkscited by 56
  5. 2020Differentiable Causal Discovery Under Unmeasured Confoundingcited by 56
  6. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  7. 2021MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanismscited by 50
  8. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 49
  9. 2018Causal Discovery in the Presence of Missing Datacited by 46
  10. 2021Identifiable Generative Models for Missing Not at Random Data Imputationcited by 30
  11. 2013The Bayesian Structural EM Algorithmcited by 26
  12. 2020Full Law Identification In Graphical Models Of Missing Data: Completeness Resultscited by 26
  13. 2019Identification In Missing Data Models Represented By Directed Acyclic Graphscited by 19
  14. 2022Reliable Causal Discovery with Improved Exact Search and Weaker Assumptionscited by 19
  15. 2020MissDeepCausal: Causal Inference from Incomplete Data Using Deep Latent Variable Modelscited by 7
  16. 2016Learning Bayesian Networks with Incomplete Data by Augmentationcited by 5

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Citing papers per year: 2022: 3; 2023: 3; 2024: 8; 2025: 4; 2026: 3.

21 papers.

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  1. 2022Harnessing Out-Of-Distribution Examples via Augmenting Content and Stylecited by 43
  2. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  3. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  4. 2024Gene Regulatory Network Inference in the Presence of Dropouts: a Causal Viewcited by 11
  5. 2024Mitigating Label Noise on Graph via Topological Sample Selectioncited by 6
  6. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  7. 2024COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Datacited by 5
  8. 2025The Robustness of Differentiable Causal Discovery in Misspecified Scenarioscited by 4
  9. 2022On the Sparse DAG Structure Learning Based on Adaptive Lassocited by 3
  10. 2023Deception by Omission: Using Adversarial Missingness to Poison Causal Structure Learningcited by 3
  11. 2023Identification of Causal Structure in the Presence of Missing Data with Additive Noise Modelcited by 3
  12. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
9 more
  1. 2025Revealing Multimodal Causality with Large Language Modelscited by 3
  2. 2024Learning Cyclic Causal Models from Incomplete Datacited by 1
  3. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  4. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  5. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  6. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0
  7. 2026PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Datacited by 0
  8. 2026Causal Modeling of Selection in Evolutioncited by 0
  9. 2026ITSY: Causal Discovery From Irregular Time-Series Datacited by 0