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Structured Matrix Completion with Applications to Genomic Data Integration

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  • Tianxi Cai
  • T. Tony Cai
  • Anru Zhang

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. Supplementary materials for this article are available online.

Suggested Citation

  • Tianxi Cai & T. Tony Cai & Anru Zhang, 2016. "Structured Matrix Completion with Applications to Genomic Data Integration," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 621-633, April.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:621-633
    DOI: 10.1080/01621459.2015.1021005
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    Cited by:

    1. Fan, Jianqing & Kim, Donggyu, 2019. "Structured volatility matrix estimation for non-synchronized high-frequency financial data," Journal of Econometrics, Elsevier, vol. 209(1), pages 61-78.
    2. Xiuli Du & Xiaohu Jiang & Jinguan Lin, 2023. "Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 975-1001, September.
    3. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    4. Dong Xia & Ming Yuan, 2021. "Statistical inferences of linear forms for noisy matrix completion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 58-77, February.
    5. Xiao, Zhen & Zhang, Qi, 2022. "Dimension reduction for block-missing data based on sparse sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).

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