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

TL;DR

This paper introduces a robust kernel regression method using a new loss function, the $ ext{ extl s}$-loss, optimized via IRLS, improving noise robustness over traditional least squares approaches.

Contribution

It proposes the $ ext{ extl s}$-loss for kernel regression, providing theoretical properties and an IRLS optimization framework for enhanced noise robustness.

Findings

The $ ext{ extl s}$-loss improves robustness to noise.

The IRLS algorithm converges reliably for the proposed methods.

Experiments demonstrate superior performance on benchmark datasets.

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.