# Identifiable Deep Latent Variable Models for MNAR Data

arXiv: https://arxiv.org/abs/2603.24771 · HTML: https://mlsanity.com/paper/2603.24771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [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)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [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)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [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)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [The Deconfounded Recommender: A Causal Inference Approach to Recommendation](https://mlsanity.com/paper/1808.06581/) (2018)
- [On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds](https://mlsanity.com/paper/2302.13183/) (2023)
- [Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model](https://mlsanity.com/paper/1909.01848/) (2019)
- [Semiparametric Estimation with Data Missing Not at Random Using an Instrumental Variable](https://mlsanity.com/paper/1607.03197/) (2016)
- [Itemwise conditionally independent nonresponse modeling for incomplete multivariate data](https://mlsanity.com/paper/1609.00656/) (2016)
- [Discrete Choice Models for Nonmonotone Nonignorable Missing Data: Identification and Inference](https://mlsanity.com/paper/1607.02631/) (2016)
- [A self-censoring model for multivariate nonignorable nonmonotone missing data](https://mlsanity.com/paper/2207.08535/) (2022)
- [Deep Generative Models: Complexity, Dimensionality, and Approximation](https://mlsanity.com/paper/2504.00820/) (2025)
- [Sequential identification of nonignorable missing data mechanisms](https://mlsanity.com/paper/1701.01395/) (2017)

## Abstract (arXiv)

Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is independent of the missing values themselves. This assumption is frequently violated in real-world scenarios, prompted by recent advances in imputation methods using deep learning to address this challenge. However, these methods neglect the crucial issue of nonparametric identifiability in missing-not-at-random (MNAR) data, which can lead to biased and unreliable results. This paper seeks to bridge this gap by proposing a novel framework based on deep latent variable models for MNAR data. Building on the assumption of conditional no self-censoring given latent variables, we establish the identifiability of the data distribution. This crucial theoretical result guarantees the feasibility of our approach. To effectively estimate unknown parameters, we develop an efficient algorithm utilizing importance-weighted autoencoders. We demonstrate, both theoretically and empirically, that our estimation process accurately recovers the ground-truth joint distribution under specific regularity conditions. Extensive simulation studies and real-world data experiments showcase the advantages of our proposed method compared to various classical and state-of-the-art approaches to missing data imputation.