Huber Regression Analysis with a Semi-Supervised Method

Yue Wang, Baobin Wang, Chaoquan Peng, Xuefeng Li and Hong Yin ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-12

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.

Keywords: robust regression; Huber loss function; reproducing kernel Hilbert space; semi-supervised data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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