# Computational Efficient and Minimax Optimal Nonignorable Matrix Completion

arXiv: https://arxiv.org/abs/2504.04016 · HTML: https://mlsanity.com/paper/2504.04016/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 5 Apr 2025.

## Builds on (most cited first, 14 of 14)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Statistical Inferences of Linear Forms for Noisy Matrix Completion](https://mlsanity.com/paper/1909.00116/) (2019)
- [Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization](https://mlsanity.com/paper/1710.08083/) (2017)
- [On Low-rank Trace Regression under General Sampling Distribution](https://mlsanity.com/paper/1904.08576/) (2019)
- [Learning from Sets of Items in Recommender Systems](https://mlsanity.com/paper/1904.12643/) (2019)
- [Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms](https://mlsanity.com/paper/2306.06443/) (2023)
- [A Likelihood Ratio Framework for High Dimensional Semiparametric Regression](https://mlsanity.com/paper/1412.2295/) (2014)
- [Matrix Completion under Low-Rank Missing Mechanism](https://mlsanity.com/paper/1812.07813/) (2018)
- [Penalized pairwise pseudo likelihood for variable selection with nonignorable missing data](https://mlsanity.com/paper/1703.06379/) (2017)
- [U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off, with Application to Network Method-of-Moments](https://mlsanity.com/paper/2306.03793/) (2023)
- [Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness](https://mlsanity.com/paper/2402.03954/) (2024)

## Abstract (arXiv)

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and column-wise matrix U-statistic loss function for the generalized nonignorable missing mechanism, a flexible and generally applicable missing mechanism which contains both ignorable and nonignorable missing mechanism assumptions. The proposed method achieves computational efficiency comparable to the existing missing-at-random approaches, while providing the near minimax optimal statistical convergence rate guarantees for the more general nonignorable missing case. We propose an accelerated proximal gradient algorithm to solve the associated optimization problem, and characterize the interaction between algorithmic and statistical convergence. Simulations and real data analyzes further support the practical utility of the proposed method.