Matrix Completion With Covariate Information

• 成果类型: Article
• 署名作者: Mao, Xiaojun; Chen, Song Xi; Wong, Raymond K. W.
• 署名单位: Iowa State University; Peking University; Peking University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1389740
• 发表日期: 2019
• 页码: 198-210
• 关键词: regularization; algorithms

摘要

This article investigates the problem of matrix completion from the corrupted data, when the additional covariates are available. Despite being seldomly considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A(0). Given a covariate matrix X with its rows representing the row covariates of A(0), we consider a column-space-decomposition model A(0) = X-0 + B-0, where (0) is a coefficient matrix and B-0 is a low-rank matrix orthogonal to X in terms of column space. This model facilitates a clear separation between the interpretable covariate effects (X-0) and the flexible hidden factor effects (B-0). Besides, our work allows the probabilities of observation to depend on the covariate matrix, and hence a missing-at-random mechanism is permitted. We propose a novel penalized estimator for A(0) by utilizing both Frobenius-norm and nuclear-norm regularizations with an efficient and scalable algorithm. Asymptotic convergence rates of the proposed estimators are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application.