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Supervised singular value decomposition and its asymptotic properties

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  • Li, Gen
  • Yang, Dan
  • Nobel, Andrew B.
  • Shen, Haipeng

Abstract

A supervised singular value decomposition (SupSVD) model has been developed for supervised dimension reduction where the low rank structure of the data of interest is potentially driven by additional variables measured on the same set of samples. The SupSVD model can make use of the information in the additional variables to accurately extract underlying structures that are more interpretable. The model is general and includes the principal component analysis model and the reduced rank regression model as two extreme cases. The model is formulated in a hierarchical fashion using latent variables, and a modified expectation–maximization algorithm for parameter estimation is developed, which is computationally efficient. The asymptotic properties for the estimated parameters are derived. We use comprehensive simulations and a real data example to illustrate the advantages of the SupSVD model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:7-17
    DOI: 10.1016/j.jmva.2015.02.016
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    References listed on IDEAS

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    Cited by:

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    4. Phuong T. Vu & Timothy V. Larson & Adam A. Szpiro, 2020. "Probabilistic predictive principal component analysis for spatially misaligned and high‐dimensional air pollution data with missing observations," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    5. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    6. Jung, Sungkyu, 2018. "Continuum directions for supervised dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 27-43.
    7. Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.

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