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High-probability bounds for the reconstruction error of PCA

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  • Milbradt, Cassandra
  • Wahl, Martin

Abstract

We derive high-probability bounds for the reconstruction error of PCA in infinite dimensions. We apply our bounds in the case that the eigenvalues of the covariance operator satisfy polynomial or exponential upper bounds.

Suggested Citation

  • Milbradt, Cassandra & Wahl, Martin, 2020. "High-probability bounds for the reconstruction error of PCA," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300444
    DOI: 10.1016/j.spl.2020.108741
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    References listed on IDEAS

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    1. Y. Yu & T. Wang & R. J. Samworth, 2015. "A useful variant of the Davis–Kahan theorem for statisticians," Biometrika, Biometrika Trust, vol. 102(2), pages 315-323.
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