Local Reweighted Kernel Regression

Estimating the irregular function with multiscale structure is a hard problem. The results achieved by the traditional kernel learning are often unsatisfactory, since underfitting and overfitting cannot be simultaneously avoided, and the performance relative to boundary is often unsatisfactory. In this paper, we investigate the data-based localized reweighted regression model under kernel trick and propose an iterative method to solve the kernel regression problem. The new framework of kernel learning approach includes two parts. First, an improved Nadaraya-Watson estimator based on blockwised approach is constructed; second, an iterative kernel learning method is introduced in a series decreased active set to choose kernels. Experiments on simulated and real data sets demonstrate that the proposed method can avoid underfitting and overfitting simultaneously and improve the performance relative to the boundary effect.