Date of this Version
Journal of the American Statistical Association
Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics, and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival. Supplementary materials for this article are available online.
This is an Accepted Manuscript of an article published by Taylor & Francis in the Journal of the American Statistical Association on 18 August 2016, available online: http://dx.doi.org/10.1080/01621459.2015.1021005.
constrained minimization, genomic data integration, low-rank matrix, matrix completion, singular value decomposition, structured matrix completion
Cai, T., Cai, T., & Zhang, A. (2016). Structured Matrix Completion with Applications to Genomic Data Integration. Journal of the American Statistical Association, 111 (514), 621-633. http://dx.doi.org/10.1080/01621459.2015.1021005
Date Posted: 25 October 2018
This document has been peer reviewed.