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J Am Stat Assoc. 2016;111(514):621-633. doi: 10.1080/01621459.2015.1021005. Epub 2016 Aug 18.

Structured Matrix Completion with Applications to Genomic Data Integration.

Author information

1
Professor of Biostatistics, Department of Biostatistics, Harvard University, Boston, MA.
2
Dorothy Silberberg Professor of Statistics, Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA.
3
Student, Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA.

Abstract

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.

KEYWORDS:

Constrained minimization; genomic data integration; low-rank matrix; matrix completion; singular value decomposition; structured matrix completion

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