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Incorporating covariates into integrated factor analysis of multi‐view data

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  • Gen Li
  • Sungkyu Jung

Abstract

In modern biomedical research, it is ubiquitous to have multiple data sets measured on the same set of samples from different views (i.e., multi‐view data). For example, in genetic studies, multiple genomic data sets at different molecular levels or from different cell types are measured for a common set of individuals to investigate genetic regulation. Integration and reduction of multi‐view data have the potential to leverage information in different data sets, and to reduce the magnitude and complexity of data for further statistical analysis and interpretation. In this article, we develop a novel statistical model, called supervised integrated factor analysis (SIFA), for integrative dimension reduction of multi‐view data while incorporating auxiliary covariates. The model decomposes data into joint and individual factors, capturing the joint variation across multiple data sets and the individual variation specific to each set, respectively. Moreover, both joint and individual factors are partially informed by auxiliary covariates via nonparametric models. We devise a computationally efficient Expectation–Maximization (EM) algorithm to fit the model under some identifiability conditions. We apply the method to the Genotype‐Tissue Expression (GTEx) data, and provide new insights into the variation decomposition of gene expression in multiple tissues. Extensive simulation studies and an additional application to a pediatric growth study demonstrate the advantage of the proposed method over competing methods.

Suggested Citation

  • Gen Li & Sungkyu Jung, 2017. "Incorporating covariates into integrated factor analysis of multi‐view data," Biometrics, The International Biometric Society, vol. 73(4), pages 1433-1442, December.
  • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1433-1442
    DOI: 10.1111/biom.12698
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    References listed on IDEAS

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    3. Li, Gen & Yang, Dan & Nobel, Andrew B. & Shen, Haipeng, 2016. "Supervised singular value decomposition and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 7-17.
    4. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    5. Shabalin, Andrey A. & Nobel, Andrew B., 2013. "Reconstruction of a low-rank matrix in the presence of Gaussian noise," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 67-76.
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    Citations

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    Cited by:

    1. Xing Gao & Sungwon Lee & Gen Li & Sungkyu Jung, 2021. "Covariate‐driven factorization by thresholding for multiblock data," Biometrics, The International Biometric Society, vol. 77(3), pages 1011-1023, September.
    2. Sangyoon Yi & Raymond Ka Wai Wong & Irina Gaynanova, 2023. "Hierarchical nuclear norm penalization for multi‐view data integration," Biometrics, The International Biometric Society, vol. 79(4), pages 2933-2946, December.
    3. Palzer, Elise F. & Wendt, Christine H. & Bowler, Russell P. & Hersh, Craig P. & Safo, Sandra E. & Lock, Eric F., 2022. "sJIVE: Supervised joint and individual variation explained," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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