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Sparse semiparametric canonical correlation analysis for data of mixed types

Author

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  • Grace Yoon
  • Raymond J Carroll
  • Irina Gaynanova

Abstract

SummaryCanonical correlation analysis investigates linear relationships between two sets of variables, but it often works poorly on modern datasets because of high dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach to sparse canonical correlation analysis based on the Gaussian copula. The main result of this paper is a truncated latent Gaussian copula model for data with excess zeros, which allows us to derive a rank-based estimator of the latent correlation matrix for mixed variable types without estimation of marginal transformation functions. The resulting canonical correlation analysis method works well in high-dimensional settings, as demonstrated via numerical studies, and when applied to the analysis of association between gene expression and microRNA data from breast cancer patients.

Suggested Citation

  • Grace Yoon & Raymond J Carroll & Irina Gaynanova, 2020. "Sparse semiparametric canonical correlation analysis for data of mixed types," Biometrika, Biometrika Trust, vol. 107(3), pages 609-625.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:3:p:609-625.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa007
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    Cited by:

    1. Bottmer, Lea & Croux, Christophe & Wilms, Ines, 2022. "Sparse regression for large data sets with outliers," European Journal of Operational Research, Elsevier, vol. 297(2), pages 782-794.
    2. Yutong Liu & Toni Darville & Xiaojing Zheng & Quefeng Li, 2023. "Decomposition of variation of mixed variables by a latent mixed Gaussian copula model," Biometrics, The International Biometric Society, vol. 79(2), pages 1187-1200, June.

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