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Huber Regression Analysis with a Semi-Supervised Method

Author

Listed:
  • Yue Wang

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China)

  • Baobin Wang

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China)

  • Chaoquan Peng

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China)

  • Xuefeng Li

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China)

  • Hong Yin

    (School of Mathematics, Renmin University of China, Beijing 100872, China)

Abstract

In this paper, we study the regularized Huber regression algorithm in a reproducing kernel Hilbert space (RKHS), which is applicable to both fully supervised and semi-supervised learning schemes. Our focus in the work is two-fold: first, we provide the convergence properties of the algorithm with fully supervised data. We establish optimal convergence rates in the minimax sense when the regression function lies in RKHSs. Second, we improve the learning performance of the Huber regression algorithm by a semi-supervised method. We show that, with sufficient unlabeled data, the minimax optimal rates can be retained if the regression function is out of RKHSs.

Suggested Citation

  • Yue Wang & Baobin Wang & Chaoquan Peng & Xuefeng Li & Hong Yin, 2022. "Huber Regression Analysis with a Semi-Supervised Method," Mathematics, MDPI, vol. 10(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3734-:d:938986
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    References listed on IDEAS

    as
    1. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
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    Cited by:

    1. Vu, Anh Ngoc, 2023. "Demand reduction campaigns for the illegal wildlife trade in authoritarian Vietnam: Ungrounded environmentalism," World Development, Elsevier, vol. 164(C).

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