mlsanityData to 14 Oct 2026

Identifiable Generative Models for Missing Not at Random Data Imputation

arXiv 2110.14708 ↗First posted 27 Oct 2021cs.LG stat.MLcited by 30

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Abstract (arXiv)

Real-world datasets often have missing values associated with complex generative processes, where the cause of the missingness may not be fully observed. This is known as missing not at random (MNAR) data. However, many imputation methods do not take into account the missingness mechanism, resulting in biased imputation values when MNAR data is present. Although there are a few methods that have considered the MNAR scenario, their model's identifiability under MNAR is generally not guaranteed. That is, model parameters can not be uniquely determined even with infinite data samples, hence the imputation results given by such models can still be biased. This issue is especially overlooked by many modern deep generative models. In this work, we fill in this gap by systematically analyzing the identifiability of generative models under MNAR. Furthermore, we propose a practical deep generative model which can provide identifiability guarantees under mild assumptions, for a wide range of MNAR mechanisms. Our method demonstrates a clear advantage for tasks on both synthetic data and multiple real-world scenarios with MNAR data.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). Builds on 19 of its 64 references that are in the map. First posted on arXiv 27 Oct 2021.

Builds on

19 of 64 references.

References · 19

  1. 2013Auto-Encoding Variational Bayescited by 4,053
  2. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  3. 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 352
  4. 2016Recommendations as Treatments: Debiasing Learning and Evaluationcited by 248
  5. 2017Advances in Variational Inferencecited by 236
  6. 2018Handling Incomplete Heterogeneous Data using VAEscited by 149
  7. 2018The Blessings of Multiple Causescited by 104
  8. 2018EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAEcited by 87
  9. 2019MisGAN: Learning from Incomplete Data with Generative Adversarial Networkscited by 75
  10. 2015Modeling User Exposure in Recommendationcited by 69
  11. 2020VAEM: a Deep Generative Model for Heterogeneous Mixed Type Datacited by 66
  12. 2020Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challengecited by 64
7 more
  1. 2020not-MIWAE: Deep Generative Modelling with Missing not at Random Datacited by 62
  2. 2018Causal Discovery in the Presence of Missing Datacited by 47
  3. 2019Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumptioncited by 29
  4. 2018Imputation and low-rank estimation with Missing Not At Random datacited by 21
  5. 2018The Deconfounded Recommender: A Causal Inference Approach to Recommendationcited by 19
  6. 2018Multiple Imputation: A Review of Practical and Theoretical Findingscited by 14
  7. 2021Variational Selective Autoencoder: Learning from Partially-Observed Heterogeneous Datacited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 6; 2023: 6; 2024: 8; 2025: 5; 2026: 4.

30 papers.

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  1. 2022HyperImpute: Generalized Iterative Imputation with Automatic Model Selectioncited by 83
  2. 2023ReMasker: Imputing Tabular Data with Masked Autoencodingcited by 37
  3. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 22
  4. 2022Conditional Generation of Medical Time Series for Extrapolation to Underrepresented Populationscited by 14
  5. 2024Review for Handling Missing Data with special missing mechanismcited by 7
  6. 2024Optimal Transport for Structure Learning Under Missing Datacited by 6
  7. 2025Robust Simulation-Based Inference under Missing Data via Neural Processescited by 5
  8. 2025Learning-To-Measure: In-Context Active Feature Acquisitioncited by 5
  9. 2021Variational Gibbs Inference for Statistical Model Estimation from Incomplete Datacited by 4
  10. 2023Identification of Causal Structure in the Presence of Missing Data with Additive Noise Modelcited by 4
  11. 2024Symmetric Matrix Completion with ReLU Samplingcited by 4
  12. 2022Leveraging variational autoencoders for multiple data imputationcited by 3
18 more
  1. 2023Identifiability Matters: Revealing the Hidden Recoverable Condition in Unbiased Learning to Rankcited by 3
  2. 2022Deeply-Learned Generalized Linear Models with Missing Datacited by 2
  3. 2024Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Familiescited by 2
  4. 2024Generative Adversarial Networks for Imputing Sparse Learning Performancecited by 2
  5. 2025Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approachescited by 2
  6. 2026Missingness-aware Data Imputation via AI-powered Bayesian Generative Modelingcited by 2
  7. 2022GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studiescited by 1
  8. 2023No Imputation Needed: A Switch Approach to Irregularly Sampled Time Seriescited by 1
  9. 2023Posterior Consistency for Missing Data in Variational Autoencoderscited by 1
  10. 2024Exploiting Missing Data Remediation Strategies using Adversarial Missingness Attackscited by 1
  11. 2024Still More Shades of Null: An Evaluation Suite for Responsible Missing Value Imputationcited by 1
  12. 2023Deep Generative Imputation Model for Missing Not At Random Datacited by 0
  13. 2024Deep Representation Learning-Based Dynamic Trajectory Phenotyping for Acute Respiratory Failure in Medical Intensive Care Unitscited by 0
  14. 2025Generative Data Imputation for Sparse Learner Performance Data Using Generative Adversarial Imputation Networkscited by 0
  15. 2025Domain Adaptation Under MNAR Missingnesscited by 0
  16. 2026Generative Conditional Missing Imputation Networkscited by 0
  17. 2026Identifiable Deep Latent Variable Models for MNAR Datacited by 0
  18. 2026Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Randomcited by 0