Kernel based regression with robust loss function via iteratively reweighted least squares
This work addresses noise robustness in regression for machine learning applications, but it is incremental as it modifies existing methods with a new loss function.
The paper tackles the noise sensitivity problem in kernel-based regression methods like LS-SVR and ELM by proposing a generalized loss function called ℓs-loss, which improves robustness, with experiments on artificial and benchmark datasets confirming its validity.
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.