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arXiv · 1903.11202

Kernel based regression with robust loss function via iteratively reweighted least squares

Hongwei Dong·Liming Yang
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Abstract

Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine (ELM) are popular techniques. However, the noise sensitivity is a major bottleneck. To address this issue, a generalized loss function, called $\ell_s$-loss, is proposed in this paper. With the support of novel loss function, two kernel based regressors are constructed by replacing the $\ell_2$-loss in LS-SVR and ELM with the proposed $\ell_s$-loss for better noise robustness. Important properties of $\ell_s$-loss, including robustness, asymmetry and asymptotic approximation behaviors, are verified theoretically. Moreover, iteratively reweighted least squares (IRLS) is utilized to optimize and interpret the proposed methods from a weighted viewpoint. The convergence of the proposal are proved, and detailed analyses of robustness are given. Experiments on both artificial and benchmark datasets confirm the validity of the proposed methods.

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Hongwei Dong, Liming Yang. 2019-03-27. Kernel based regression with robust loss function via iteratively reweighted least squares. https://arxiv.org/abs/1903.11202

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