arXiv subjects

Yuanhong A

Publications and source records attributed to Yuanhong A.

2 recordsLinked to original sources

arXiv2025

Computational Efficient and Minimax Optimal Nonignorable Matrix Completion

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.

stat.ML↗

arXiv2025

Leveraging Shared Factor Structures for Enhanced Matrix Completion with Nonconvex Penalty Regularization

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development in matrix completion, the potential relationship between observed data and missing indicators has largely been overlooked. To address this gap, we propose a joint modeling framework for the observed data and missing indicators within the context of a generalized factor model and derive the asymptotic limit distribution of the estimators. Furthermore, to tackle the rank estimation problem for model specification, we employ matrix nonconvex penalty regularization and establish nonasymptotic probability guarantees for the Oracle property. The theoretical results are validated through extensive simulation studies and real-world data analysis, demonstrating the effectiveness of the proposed method.

stat.ME↗