# Deep Generative Imputation Model for Missing Not At Random Data

arXiv: https://arxiv.org/abs/2308.08158 · HTML: https://mlsanity.com/paper/2308.08158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [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)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [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)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [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)
- [AutoDebias: Learning to Debias for Recommendation](https://mlsanity.com/paper/2105.04170/) (2021)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [Information Theoretic Counterfactual Learning from Missing-Not-At-Random Feedback](https://mlsanity.com/paper/2009.02623/) (2020)
- [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)
- [Asymmetric Tri-training for Debiasing Missing-Not-At-Random Explicit Feedback](https://mlsanity.com/paper/1910.01444/) (2019)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Variational Selective Autoencoder: Learning from Partially-Observed Heterogeneous Data](https://mlsanity.com/paper/2102.12679/) (2021)

## Abstract (arXiv)

Data analysis usually suffers from the Missing Not At Random (MNAR) problem, where the cause of the value missing is not fully observed. Compared to the naive Missing Completely At Random (MCAR) problem, it is more in line with the realistic scenario whereas more complex and challenging. Existing statistical methods model the MNAR mechanism by different decomposition of the joint distribution of the complete data and the missing mask. But we empirically find that directly incorporating these statistical methods into deep generative models is sub-optimal. Specifically, it would neglect the confidence of the reconstructed mask during the MNAR imputation process, which leads to insufficient information extraction and less-guaranteed imputation quality. In this paper, we revisit the MNAR problem from a novel perspective that the complete data and missing mask are two modalities of incomplete data on an equal footing. Along with this line, we put forward a generative-model-specific joint probability decomposition method, conjunction model, to represent the distributions of two modalities in parallel and extract sufficient information from both complete data and missing mask. Taking a step further, we exploit a deep generative imputation model, namely GNR, to process the real-world missing mechanism in the latent space and concurrently impute the incomplete data and reconstruct the missing mask. The experimental results show that our GNR surpasses state-of-the-art MNAR baselines with significant margins (averagely improved from 9.9% to 18.8% in RMSE) and always gives a better mask reconstruction accuracy which makes the imputation more principle.