# not-MIWAE: Deep Generative Modelling with Missing not at Random Data

arXiv: https://arxiv.org/abs/2006.12871 · HTML: https://mlsanity.com/paper/2006.12871/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 30 of 62)

- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Probabilistic Imputation for Time-series Classification with Missing Data](https://mlsanity.com/paper/2308.06738/) (2023)
- [Model-agnostic out-of-distribution detection using combined statistical tests](https://mlsanity.com/paper/2203.01097/) (2022)
- [Learning Conditional Variational Autoencoders with Missing Covariates](https://mlsanity.com/paper/2203.01218/) (2022)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [A Brief Overview of Unsupervised Neural Speech Representation Learning](https://mlsanity.com/paper/2203.01829/) (2022)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models](https://mlsanity.com/paper/2106.04804/) (2021)
- [Differentiable and Scalable Generative Adversarial Models for Data Imputation](https://mlsanity.com/paper/2201.03202/) (2022)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data](https://mlsanity.com/paper/2111.13180/) (2021)
- [Posterior Matching for Arbitrary Conditioning](https://mlsanity.com/paper/2201.12414/) (2022)
- [FragmGAN: Generative Adversarial Nets for Fragmentary Data Imputation and Prediction](https://mlsanity.com/paper/2203.04692/) (2022)
- [Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives](https://mlsanity.com/paper/2309.00380/) (2023)
- [CACTI: Leveraging Copy Masking and Contextual Information to Improve Tabular Data Imputation](https://mlsanity.com/paper/2506.02306/) (2025)
- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)
- [Deep Generative Pattern-Set Mixture Models for Nonignorable Missingness](https://mlsanity.com/paper/2103.03532/) (2021)
- [Uphill Roads to Variational Tightness: Monotonicity and Monte Carlo Objectives](https://mlsanity.com/paper/2201.10989/) (2022)
- [Interpretable Models Capable of Handling Systematic Missingness in Imbalanced Classes and Heterogeneous Datasets](https://mlsanity.com/paper/2206.02056/) (2022)
- [Leveraging variational autoencoders for multiple data imputation](https://mlsanity.com/paper/2209.15321/) (2022)
- [Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data](https://mlsanity.com/paper/2211.13297/) (2022)
- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [Reconstruction of Incomplete Wildfire Data using Deep Generative Models](https://mlsanity.com/paper/2201.06153/) (2022)
- [Generative Adversarial Classification Network with Application to Network Traffic Classification](https://mlsanity.com/paper/2303.10681/) (2023)
- [Fed-MIWAE: Federated Imputation of Incomplete Data via Deep Generative Models](https://mlsanity.com/paper/2304.08054/) (2023)
- [Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Families](https://mlsanity.com/paper/2403.03069/) (2024)

## Abstract (arXiv)

When a missing process depends on the missing values themselves, it needs to be explicitly modelled and taken into account while doing likelihood-based inference. We present an approach for building and fitting deep latent variable models (DLVMs) in cases where the missing process is dependent on the missing data. Specifically, a deep neural network enables us to flexibly model the conditional distribution of the missingness pattern given the data. This allows for incorporating prior information about the type of missingness (e.g. self-censoring) into the model. Our inference technique, based on importance-weighted variational inference, involves maximising a lower bound of the joint likelihood. Stochastic gradients of the bound are obtained by using the reparameterisation trick both in latent space and data space. We show on various kinds of data sets and missingness patterns that explicitly modelling the missing process can be invaluable.