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Robust covariance estimation for distributed principal component analysis

Author

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  • Kangqiang Li

    (Zhejiang University)

  • Han Bao

    (Zhejiang University)

  • Lixin Zhang

    (Zhejiang University)

Abstract

Fan et al. (Ann Stat 47(6):3009–3031, 2019) constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers significantly. However, their algorithm’s guarantee is only for sub-Gaussian data. Spurred by this deficiency, this paper enhances the effectiveness of their distributed PCA algorithm by utilizing robust covariance matrix estimators of Minsker (Ann Stat 46(6A):2871–2903, 2018) and Ke et al. (Stat Sci 34(3):454–471, 2019) to tame heavy-tailed data. The theoretical results demonstrate that when the sampling distribution is symmetric innovation with the bounded fourth moment or asymmetric with the finite 6th moment, the statistical error rate of the final estimator produced by the robust algorithm is similar to that of sub-Gaussian tails. Extensive numerical trials support the theoretical analysis and indicate that our algorithm is robust to heavy-tailed data and outliers.

Suggested Citation

  • Kangqiang Li & Han Bao & Lixin Zhang, 2022. "Robust covariance estimation for distributed principal component analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 707-732, August.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:6:d:10.1007_s00184-021-00848-9
    DOI: 10.1007/s00184-021-00848-9
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    References listed on IDEAS

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    1. Fang Han & Han Liu, 2018. "ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 252-268, January.
    2. Marco Avella-Medina & Heather S Battey & Jianqing Fan & Quefeng Li, 2018. "Robust estimation of high-dimensional covariance and precision matrices," Biometrika, Biometrika Trust, vol. 105(2), pages 271-284.
    3. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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    1. Kenji Katayama & Kei Kawaguchi & Yuta Egawa & Zhenhua Pan, 2022. "Local Charge Carrier Dynamics for Photocatalytic Materials Using Pattern-Illumination Time-Resolved Phase Microscopy," Energies, MDPI, vol. 15(24), pages 1-13, December.

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