Iteratively reweighted least squares for robust regression via SVM and ELM

The measure of most robust machine learning methods is reweighted. To overcome the optimization difficulty of the implicitly reweighted robust methods (including modifying loss functions and objectives), we try to use a more direct method: explicitly iteratively reweighted method to handle noise (even heavy-tailed noise and outlier) robustness. In this paper, an explicitly iterative reweighted framework based on two kinds of kernel based regression algorithm (LS-SVR and ELM) is established, and a novel weight selection strategy is proposed at the same time. Combining the proposed weight function with the iteratively reweighted framework, we propose two models iteratively reweighted least squares support vector machine (IRLS-SVR) and iteratively reweighted extreme learning machine (IRLS-ELM) to implement robust regression. Different from the traditional explicitly reweighted robust methods, we carry out multiple reweighted operations in our work to further improve robustness. The convergence and approximability of the proposed algorithms are proved theoretically. Moreover, the robustness of the algorithm is analyzed in detail from many angles. Experiments on both artificial data and benchmark datasets confirm the validity of the proposed methods.