# MIWAE: Deep Generative Modelling and Imputation of Incomplete Data

arXiv: https://arxiv.org/abs/1812.02633 · HTML: https://mlsanity.com/paper/1812.02633/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2018.

## Built on by (most cited first, 14 of 14)

- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [Fairness in Missing Data Imputation](https://mlsanity.com/paper/2110.12002/) (2021)
- [DiffImpute: Tabular Data Imputation With Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2403.13863/) (2024)
- [CACTI: Leveraging Copy Masking and Contextual Information to Improve Tabular Data Imputation](https://mlsanity.com/paper/2506.02306/) (2025)
- [Explainable Data Imputation using Constraints](https://mlsanity.com/paper/2205.04731/) (2022)
- [Robust prediction under missingness shifts](https://mlsanity.com/paper/2406.16484/) (2024)
- [Training Deep Normalizing Flow Models in Highly Incomplete Data Scenarios with Prior Regularization](https://mlsanity.com/paper/2104.01482/) (2021)
- [Unsupervised domain adaptation with non-stochastic missing data](https://mlsanity.com/paper/2109.09505/) (2021)
- [Variational Autoencoding of Dental Point Clouds](https://mlsanity.com/paper/2307.10895/) (2023)
- [Scalable Numerical Embeddings for Multivariate Time Series: Enhancing Healthcare Data Representation Learning](https://mlsanity.com/paper/2405.16557/) (2024)
- [MISNN: Multiple Imputation via Semi-parametric Neural Networks](https://mlsanity.com/paper/2305.01794/) (2023)
- [Latent Diffusion for Missing Data](https://mlsanity.com/paper/2605.28427/) (2026)
- [Marformer: A Transformer for Predicting Missing Data Distributions](https://mlsanity.com/paper/2610.12379/) (2026)

## Abstract (arXiv)

We consider the problem of handling missing data with deep latent variable models (DLVMs). First, we present a simple technique to train DLVMs when the training set contains missing-at-random data. Our approach, called MIWAE, is based on the importance-weighted autoencoder (IWAE), and maximises a potentially tight lower bound of the log-likelihood of the observed data. Compared to the original IWAE, our algorithm does not induce any additional computational overhead due to the missing data. We also develop Monte Carlo techniques for single and multiple imputation using a DLVM trained on an incomplete data set. We illustrate our approach by training a convolutional DLVM on a static binarisation of MNIST that contains 50% of missing pixels. Leveraging multiple imputation, a convolutional network trained on these incomplete digits has a test performance similar to one trained on complete data. On various continuous and binary data sets, we also show that MIWAE provides accurate single imputations, and is highly competitive with state-of-the-art methods.