# Imputation and low-rank estimation with Missing Not At Random data

arXiv: https://arxiv.org/abs/1812.11409 · HTML: https://mlsanity.com/paper/1812.11409/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2018.

## Built on by (most cited first, 21 of 21)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Be Causal: De-biasing Social Network Confounding in Recommendation](https://mlsanity.com/paper/2105.07775/) (2021)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Symmetric Matrix Completion with ReLU Sampling](https://mlsanity.com/paper/2406.05822/) (2024)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)
- [Riemannian classification of EEG signals with missing values](https://mlsanity.com/paper/2110.10011/) (2021)
- [Model-based Clustering with Missing Not At Random Data](https://mlsanity.com/paper/2112.10425/) (2021)
- [Density Ratio Estimation and Neyman Pearson Classification with Missing Data](https://mlsanity.com/paper/2302.10655/) (2023)
- [Exploiting Observation Bias to Improve Matrix Completion](https://mlsanity.com/paper/2306.04775/) (2023)
- [Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion](https://mlsanity.com/paper/2411.12965/) (2024)
- [IVGAE: Handling Incomplete Heterogeneous Data with a Variational Graph Autoencoder](https://mlsanity.com/paper/2511.22116/) (2025)
- [Time-Series Imputation with Wasserstein Interpolation for Optimal Look-Ahead-Bias and Variance Tradeoff](https://mlsanity.com/paper/2102.12736/) (2021)
- [Learning to Recommend Using Non-Uniform Data](https://mlsanity.com/paper/2110.11248/) (2021)
- [SparGE: Sparse Coding-based Patient Similarity Learning via Low-rank Constraints and Graph Embedding](https://mlsanity.com/paper/2202.01427/) (2022)
- [Deep Generative Imputation Model for Missing Not At Random Data](https://mlsanity.com/paper/2308.08158/) (2023)
- [Computational Efficient and Minimax Optimal Nonignorable Matrix Completion](https://mlsanity.com/paper/2504.04016/) (2025)
- [Truncated Matrix Completion - An Empirical Study](https://mlsanity.com/paper/2504.09873/) (2025)
- [Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors](https://mlsanity.com/paper/2603.11942/) (2026)

## Abstract (arXiv)

Missing values challenge data analysis because many supervised and unsupervised learning methods cannot be applied directly to incomplete data. Matrix completion based on low-rank assumptions are very powerful solution for dealing with missing values. However, existing methods do not consider the case of informative missing values which are widely encountered in practice. This paper proposes matrix completion methods to recover Missing Not At Random (MNAR) data. Our first contribution is to suggest a model-based estimation strategy by modelling the missing mechanism distribution. An EM algorithm is then implemented, involving a Fast Iterative Soft-Thresholding Algorithm (FISTA). Our second contribution is to suggest a computationally efficient surrogate estimation by implicitly taking into account the joint distribution of the data and the missing mechanism: the data matrix is concatenated with the mask coding for the missing values; a low-rank structure for exponential family is assumed on this new matrix, in order to encode links between variables and missing mechanisms. The methodology that has the great advantage of handling different missing value mechanisms is robust to model specification errors.The performances of our methods are assessed on the real data collected from a trauma registry (TraumaBase ) containing clinical information about over twenty thousand severely traumatized patients in France. The aim is then to predict if the doctors should administrate tranexomic acid to patients with traumatic brain injury, that would limit excessive bleeding.