# EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models

arXiv: https://arxiv.org/abs/2106.04804 · HTML: https://mlsanity.com/paper/2106.04804/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators](https://mlsanity.com/paper/2006.11469/) (2020)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [MIDA: Multiple Imputation using Denoising Autoencoders](https://mlsanity.com/paper/1705.02737/) (2017)
- [Multiple imputation for continuous variables using a Bayesian principal component analysis](https://mlsanity.com/paper/1401.5747/) (2014)

## Built on by (most cited first, 6 of 6)

- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Deep Reinforcement Learning for Cost-Effective Medical Diagnosis](https://mlsanity.com/paper/2302.10261/) (2023)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Models](https://mlsanity.com/paper/2405.17712/) (2024)
- [NeuralPrefix: A Zero-shot Sensory Data Imputation Plugin](https://mlsanity.com/paper/2502.05883/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

The presence of missing values within high-dimensional data is an ubiquitous problem for many applied sciences. A serious limitation of many available data mining and machine learning methods is their inability to handle partially missing values and so an integrated approach that combines imputation and model estimation is vital for down-stream analysis. A computationally fast algorithm, called EMFlow, is introduced that performs imputation in a latent space via an online version of Expectation-Maximization (EM) algorithm by using a normalizing flow (NF) model which maps the data space to a latent space. The proposed EMFlow algorithm is iterative, involving updating the parameters of online EM and NF alternatively. Extensive experimental results for high-dimensional multivariate and image datasets are presented to illustrate the superior performance of the EMFlow compared to a couple of recently available methods in terms of both predictive accuracy and speed of algorithmic convergence. We provide code for all our experiments.