# VAEs in the Presence of Missing Data

arXiv: https://arxiv.org/abs/2006.05301 · HTML: https://mlsanity.com/paper/2006.05301/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

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

- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [Variational Selective Autoencoder: Learning from Partially-Observed Heterogeneous Data](https://mlsanity.com/paper/2102.12679/) (2021)
- [Learning Conditional Variational Autoencoders with Missing Covariates](https://mlsanity.com/paper/2203.01218/) (2022)
- [EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models](https://mlsanity.com/paper/2106.04804/) (2021)
- [How to Sense the World: Leveraging Hierarchy in Multimodal Perception for Robust Reinforcement Learning Agents](https://mlsanity.com/paper/2110.03608/) (2021)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Medical data wrangling with sequential variational autoencoders](https://mlsanity.com/paper/2103.07206/) (2021)
- [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)
- [Predictive World Models from Real-World Partial Observations](https://mlsanity.com/paper/2301.04783/) (2023)
- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [Deep Generative Pattern-Set Mixture Models for Nonignorable Missingness](https://mlsanity.com/paper/2103.03532/) (2021)
- [Leveraging variational autoencoders for multiple data imputation](https://mlsanity.com/paper/2209.15321/) (2022)
- [Conditional expectation with regularization for missing data imputation](https://mlsanity.com/paper/2302.00911/) (2023)
- [Sampling-guided Heterogeneous Graph Neural Network with Temporal Smoothing for Scalable Longitudinal Data Imputation](https://mlsanity.com/paper/2411.04899/) (2024)
- [Missingness-aware Data Imputation via AI-powered Bayesian Generative Modeling](https://mlsanity.com/paper/2605.01676/) (2026)
- [PROMISSING: Pruning Missing Values in Neural Networks](https://mlsanity.com/paper/2206.01640/) (2022)
- [Posterior Consistency for Missing Data in Variational Autoencoders](https://mlsanity.com/paper/2310.16648/) (2023)
- [Latent variable model for high-dimensional point process with structured missingness](https://mlsanity.com/paper/2402.05758/) (2024)
- [IVGAE: Handling Incomplete Heterogeneous Data with a Variational Graph Autoencoder](https://mlsanity.com/paper/2511.22116/) (2025)
- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Masking](https://mlsanity.com/paper/2606.03347/) (2026)
- [Deep Generative Imputation Model for Missing Not At Random Data](https://mlsanity.com/paper/2308.08158/) (2023)
- [A Vector-Quantized Foundation Model for Patient Behavior Monitoring](https://mlsanity.com/paper/2503.15221/) (2025)
- [Masked Conditioning for Deep Generative Models](https://mlsanity.com/paper/2505.16725/) (2025)
- [Missing-Modality-Aware Graph Neural Network for Cancer Classification](https://mlsanity.com/paper/2506.22901/) (2025)
- [Meta-Imputation Balanced (MIB): An Ensemble Approach for Handling Missing Data in Biomedical Machine Learning](https://mlsanity.com/paper/2509.03316/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Amortized Variational Inference for Logistic Regression with Missing Covariates](https://mlsanity.com/paper/2603.21244/) (2026)

## Abstract (arXiv)

Real world datasets often contain entries with missing elements e.g. in a medical dataset, a patient is unlikely to have taken all possible diagnostic tests. Variational Autoencoders (VAEs) are popular generative models often used for unsupervised learning. Despite their widespread use it is unclear how best to apply VAEs to datasets with missing data. We develop a novel latent variable model of a corruption process which generates missing data, and derive a corresponding tractable evidence lower bound (ELBO). Our model is straightforward to implement, can handle both missing completely at random (MCAR) and missing not at random (MNAR) data, scales to high dimensional inputs and gives both the VAE encoder and decoder principled access to indicator variables for whether a data element is missing or not. On the MNIST and SVHN datasets we demonstrate improved marginal log-likelihood of observed data and better missing data imputation, compared to existing approaches.