# Identifiable Generative Models for Missing Not at Random Data Imputation

arXiv: https://arxiv.org/abs/2110.14708 · HTML: https://mlsanity.com/paper/2110.14708/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 64 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [Modeling User Exposure in Recommendation](https://mlsanity.com/paper/1510.07025/) (2015)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2007.12061/) (2020)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [The Deconfounded Recommender: A Causal Inference Approach to Recommendation](https://mlsanity.com/paper/1808.06581/) (2018)
- [Multiple Imputation: A Review of Practical and Theoretical Findings](https://mlsanity.com/paper/1801.04058/) (2018)
- [Variational Selective Autoencoder: Learning from Partially-Observed Heterogeneous Data](https://mlsanity.com/paper/2102.12679/) (2021)

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

- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Conditional Generation of Medical Time Series for Extrapolation to Underrepresented Populations](https://mlsanity.com/paper/2201.08186/) (2022)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Learning-To-Measure: In-Context Active Feature Acquisition](https://mlsanity.com/paper/2510.12624/) (2025)
- [Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data](https://mlsanity.com/paper/2111.13180/) (2021)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [Symmetric Matrix Completion with ReLU Sampling](https://mlsanity.com/paper/2406.05822/) (2024)
- [Leveraging variational autoencoders for multiple data imputation](https://mlsanity.com/paper/2209.15321/) (2022)
- [Identifiability Matters: Revealing the Hidden Recoverable Condition in Unbiased Learning to Rank](https://mlsanity.com/paper/2309.15560/) (2023)
- [Deeply-Learned Generalized Linear Models with Missing Data](https://mlsanity.com/paper/2207.08911/) (2022)
- [Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Families](https://mlsanity.com/paper/2403.03069/) (2024)
- [Generative Adversarial Networks for Imputing Sparse Learning Performance](https://mlsanity.com/paper/2407.18875/) (2024)
- [Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approaches](https://mlsanity.com/paper/2506.01696/) (2025)
- [Missingness-aware Data Imputation via AI-powered Bayesian Generative Modeling](https://mlsanity.com/paper/2605.01676/) (2026)
- [GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studies](https://mlsanity.com/paper/2210.07416/) (2022)
- [No Imputation Needed: A Switch Approach to Irregularly Sampled Time Series](https://mlsanity.com/paper/2309.08698/) (2023)
- [Posterior Consistency for Missing Data in Variational Autoencoders](https://mlsanity.com/paper/2310.16648/) (2023)
- [Exploiting Missing Data Remediation Strategies using Adversarial Missingness Attacks](https://mlsanity.com/paper/2409.04407/) (2024)
- [Still More Shades of Null: An Evaluation Suite for Responsible Missing Value Imputation](https://mlsanity.com/paper/2409.07510/) (2024)
- [Deep Generative Imputation Model for Missing Not At Random Data](https://mlsanity.com/paper/2308.08158/) (2023)
- [Deep Representation Learning-Based Dynamic Trajectory Phenotyping for Acute Respiratory Failure in Medical Intensive Care Units](https://mlsanity.com/paper/2405.02563/) (2024)
- [Generative Data Imputation for Sparse Learner Performance Data Using Generative Adversarial Imputation Networks](https://mlsanity.com/paper/2503.18982/) (2025)
- [Domain Adaptation Under MNAR Missingness](https://mlsanity.com/paper/2504.00322/) (2025)
- [Generative Conditional Missing Imputation Networks](https://mlsanity.com/paper/2601.00517/) (2026)
- [Identifiable Deep Latent Variable Models for MNAR Data](https://mlsanity.com/paper/2603.24771/) (2026)
- [Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Random](https://mlsanity.com/paper/2605.25439/) (2026)

## Abstract (arXiv)

Real-world datasets often have missing values associated with complex generative processes, where the cause of the missingness may not be fully observed. This is known as missing not at random (MNAR) data. However, many imputation methods do not take into account the missingness mechanism, resulting in biased imputation values when MNAR data is present. Although there are a few methods that have considered the MNAR scenario, their model's identifiability under MNAR is generally not guaranteed. That is, model parameters can not be uniquely determined even with infinite data samples, hence the imputation results given by such models can still be biased. This issue is especially overlooked by many modern deep generative models. In this work, we fill in this gap by systematically analyzing the identifiability of generative models under MNAR. Furthermore, we propose a practical deep generative model which can provide identifiability guarantees under mild assumptions, for a wide range of MNAR mechanisms. Our method demonstrates a clear advantage for tasks on both synthetic data and multiple real-world scenarios with MNAR data.