Huber Regression Analysis with a Semi-Supervised Method

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