Structured Matrix Completion with Applications to Genomic Data Integration

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 independ...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2016-06, Vol.111 (514), p.621-633
Main Authors: Cai, Tianxi, Cai, T. Tony, Zhang, Anru
Format: Article
Language:English
Subjects:
animal ovaries
Constrained minimization
engineering
equations
Genomic data integration
Genomics
Low-rank matrix
mathematics
Matrix
Matrix completion
Ovarian cancer
ovarian neoplasms
prediction
Sampling
Simulation
Singular value decomposition
Statistics
Structured matrix completion
Theory and Methods
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Summary: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.
ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2015.1021005