# Transformed Distribution Matching for Missing Value Imputation

arXiv: https://arxiv.org/abs/2302.10363 · HTML: https://mlsanity.com/paper/2302.10363/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 91 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 30 of 54)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [OTA: Optimal Transport Assignment for Object Detection](https://mlsanity.com/paper/2103.14259/) (2021)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Excessive Invariance Causes Adversarial Vulnerability](https://mlsanity.com/paper/1811.00401/) (2018)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)

## Built on by (most cited first, 30 of 31)

- [LLM-Forest: Ensemble Learning of LLMs with Graph-Augmented Prompts for Data Imputation](https://mlsanity.com/paper/2410.21520/) (2024)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [LLM Reading Tea Leaves: Automatically Evaluating Topic Models with Large Language Models](https://mlsanity.com/paper/2406.09008/) (2024)
- [On LLM-Enhanced Mixed-Type Data Imputation with High-Order Message Passing](https://mlsanity.com/paper/2501.02191/) (2025)
- [Neural Topic Modeling with Large Language Models in the Loop](https://mlsanity.com/paper/2411.08534/) (2024)
- [Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.10995/) (2024)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [Missing Data Imputation by Reducing Mutual Information with Rectified Flows](https://mlsanity.com/paper/2505.11749/) (2025)
- [A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Models](https://mlsanity.com/paper/2405.17712/) (2024)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Features](https://mlsanity.com/paper/2601.22816/) (2026)
- [Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow](https://mlsanity.com/paper/2406.15762/) (2024)
- [Impute-MACFM: Imputation based on Mask-Aware Flow Matching](https://mlsanity.com/paper/2509.23126/) (2025)
- [Scalable Numerical Embeddings for Multivariate Time Series: Enhancing Healthcare Data Representation Learning](https://mlsanity.com/paper/2405.16557/) (2024)
- [Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesis](https://mlsanity.com/paper/2405.20602/) (2024)
- [Still More Shades of Null: An Evaluation Suite for Responsible Missing Value Imputation](https://mlsanity.com/paper/2409.07510/) (2024)
- [mDAE : modified Denoising AutoEncoder for missing data imputation](https://mlsanity.com/paper/2411.12847/) (2024)
- [OASIS: Harnessing Diffusion Adversarial Network for Ocean Salinity Imputation using Sparse Drifter Trajectories](https://mlsanity.com/paper/2508.21570/) (2025)
- [A parameter-free clustering algorithm for missing datasets](https://mlsanity.com/paper/2404.05363/) (2024)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [IMAGIC-500: IMputation benchmark on A Generative Imaginary Country (500k samples)](https://mlsanity.com/paper/2506.08844/) (2025)
- [Leveraging AI Graders for Missing Score Imputation to Achieve Accurate Ability Estimation in Constructed-Response Tests](https://mlsanity.com/paper/2506.20119/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Nearly Optimal Bayesian Inference for Structural Missingness](https://mlsanity.com/paper/2601.18500/) (2026)
- [Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective](https://mlsanity.com/paper/2602.01182/) (2026)
- [Theoretical Analysis of Measure Consistency Regularization for Partially Observed Data](https://mlsanity.com/paper/2602.01437/) (2026)
- [Harpoon: Generalised Manifold Guidance for Conditional Tabular Diffusion](https://mlsanity.com/paper/2602.07875/) (2026)
- [Neural Optimal Transport in Hilbert Spaces: Characterizing Spurious Solutions and Gaussian Smoothing](https://mlsanity.com/paper/2602.14086/) (2026)
- [Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Random](https://mlsanity.com/paper/2605.25439/) (2026)
- [SafeImpute: Reliable Clinical Data Imputation via Conformal Selection](https://mlsanity.com/paper/2607.05613/) (2026)

## Abstract (arXiv)

We study the problem of imputing missing values in a dataset, which has important applications in many domains. The key to missing value imputation is to capture the data distribution with incomplete samples and impute the missing values accordingly. In this paper, by leveraging the fact that any two batches of data with missing values come from the same data distribution, we propose to impute the missing values of two batches of samples by transforming them into a latent space through deep invertible functions and matching them distributionally. To learn the transformations and impute the missing values simultaneously, a simple and well-motivated algorithm is proposed. Our algorithm has fewer hyperparameters to fine-tune and generates high-quality imputations regardless of how missing values are generated. Extensive experiments over a large number of datasets and competing benchmark algorithms show that our method achieves state-of-the-art performance.