# Missing Data Imputation using Optimal Transport

arXiv: https://arxiv.org/abs/2002.03860 · HTML: https://mlsanity.com/paper/2002.03860/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 30 of 100)

- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [Generative Table Pre-training Empowers Models for Tabular Prediction](https://mlsanity.com/paper/2305.09696/) (2023)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Classification of datasets with imputed missing values: does imputation quality matter?](https://mlsanity.com/paper/2206.08478/) (2022)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics](https://mlsanity.com/paper/2202.10723/) (2022)
- [Self-Supervision Improves Diffusion Models for Tabular Data Imputation](https://mlsanity.com/paper/2407.18013/) (2024)
- [Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problems](https://mlsanity.com/paper/2112.11507/) (2021)
- [Data Imputation with Iterative Graph Reconstruction](https://mlsanity.com/paper/2212.02810/) (2022)
- [Diffusion Models for Tabular Data Imputation and Synthetic Data Generation](https://mlsanity.com/paper/2407.02549/) (2024)
- [Imputation for prediction: beware of diminishing returns](https://mlsanity.com/paper/2407.19804/) (2024)
- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification](https://mlsanity.com/paper/2205.13573/) (2022)
- [On LLM-Enhanced Mixed-Type Data Imputation with High-Order Message Passing](https://mlsanity.com/paper/2501.02191/) (2025)
- [Scalable Unbalanced Sobolev Transport for Measures on a Graph](https://mlsanity.com/paper/2302.12498/) (2023)
- [DAEMA: Denoising Autoencoder with Mask Attention](https://mlsanity.com/paper/2106.16057/) (2021)
- [Minimizing f-Divergences by Interpolating Velocity Fields](https://mlsanity.com/paper/2305.15577/) (2023)
- [Generative Trees: Adversarial and Copycat](https://mlsanity.com/paper/2201.11205/) (2022)
- [EGG-GAE: scalable graph neural networks for tabular data imputation](https://mlsanity.com/paper/2210.10446/) (2022)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [Importance Sparsification for Sinkhorn Algorithm](https://mlsanity.com/paper/2306.06581/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)

## 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.