mlsanityData to 7 Oct 2026

Missing Data Imputation using Optimal Transport

arXiv 2002.03860 ↗First posted 10 Feb 2020stat.ML cs.LGcited by 99

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Abstract (arXiv)

Missing data is a crucial issue when applying machine learning algorithms to real-world datasets. Starting from the simple assumption that two batches extracted randomly from the same dataset should share the same distribution, we leverage optimal transport distances to quantify that criterion and turn it into a loss function to impute missing data values. We propose practical methods to minimize these losses using end-to-end learning, that can exploit or not parametric assumptions on the underlying distributions of values. We evaluate our methods on datasets from the UCI repository, in MCAR, MAR and MNAR settings. These experiments show that OT-based methods match or out-perform state-of-the-art imputation methods, even for high percentages of missing values.

Key facts. Cited by 99 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Feb 2020.

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Citing papers per year: 2021: 10; 2022: 15; 2023: 14; 2024: 23; 2025: 18; 2026: 19.

99 papers.

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  1. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  2. 2022HyperImpute: Generalized Iterative Imputation with Automatic Model Selectioncited by 81
  3. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  4. 2023Generative Table Pre-training Empowers Models for Tabular Predictioncited by 55
  5. 2021MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanismscited by 50
  6. 2023MissDiff: Training Diffusion Models on Tabular Data with Missing Valuescited by 38
  7. 2023ReMasker: Imputing Tabular Data with Masked Autoencodingcited by 35
  8. 2023Transformed Distribution Matching for Missing Value Imputationcited by 31
  9. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  10. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  11. 2022Classification of datasets with imputed missing values: does imputation quality matter?cited by 21
  12. 2022Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metricscited by 18
38 more
  1. 2024DiffPuter: Empowering Diffusion Models for Missing Data Imputationcited by 17
  2. 2024Self-Supervision Improves Diffusion Models for Tabular Data Imputationcited by 16
  3. 2021Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problemscited by 15
  4. 2022Data Imputation with Iterative Graph Reconstructioncited by 15
  5. 2024Diffusion Models for Tabular Data Imputation and Synthetic Data Generationcited by 15
  6. 2022Handling Missing Data via Max-Entropy Regularized Graph Autoencodercited by 12
  7. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  8. 2024Imputation for prediction: beware of diminishing returnscited by 11
  9. 2025On LLM-Enhanced Mixed-Type Data Imputation with High-Order Message Passingcited by 11
  10. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
  11. 2021DAEMA: Denoising Autoencoder with Mask Attentioncited by 8
  12. 2023Minimizing f-Divergences by Interpolating Velocity Fieldscited by 8
  13. 2022Generative Trees: Adversarial and Copycatcited by 7
  14. 2022EGG-GAE: scalable graph neural networks for tabular data imputationcited by 7
  15. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  16. 2024Review for Handling Missing Data with special missing mechanismcited by 7
  17. 2023Importance Sparsification for Sinkhorn Algorithmcited by 6
  18. 2025OCL: Ordinal Contrastive Learning for Imputating Features with Progressive Labelscited by 6
  19. 2025Missing Data Imputation by Reducing Mutual Information with Rectified Flowscited by 6
  20. 2022Differentiable and Scalable Generative Adversarial Models for Data Imputationcited by 5
  21. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  22. 2024A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Modelscited by 5
  23. 2024Scaling Up Diffusion and Flow-based XGBoost Modelscited by 5
  24. 2025Robust Simulation-Based Inference under Missing Data via Neural Processescited by 5
  25. 2021Disambiguation of weak supervision with exponential convergence ratescited by 4
  26. 2021Variational Gibbs Inference for Statistical Model Estimation from Incomplete Datacited by 4
  27. 2023Match-And-Deform: Time Series Domain Adaptation through Optimal Transport and Temporal Alignmentcited by 4
  28. 2024Unmasking Trees for Tabular Datacited by 4
  29. 2024Diffusion-nested Auto-Regressive Synthesis of Heterogeneous Tabular Datacited by 4
  30. 2025Imputation-Powered Inferencecited by 4
  31. 2026Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Featurescited by 4
  32. 2021Wasserstein Graph Neural Networks for Graphs with Missing Attributescited by 3
  33. 2022Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Datacited by 3
  34. 2023Numerical Data Imputation for Multimodal Data Sets: A Probabilistic Nearest-Neighbor Kernel Density Approachcited by 3
  35. 2024MagiNet: Mask-Aware Graph Imputation Network for Incomplete Traffic Datacited by 3
  36. 2024Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flowcited by 3
  37. 2024Multi-scale Temporal Fusion Transformer for Incomplete Vehicle Trajectory Predictioncited by 3
  38. 2025Incomplete Graph Learning: A Comprehensive Surveycited by 3

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