Irregular Function Estimation with LR-MKR

Estimating the irregular function with multi-scale 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 local reweighted regression model under kernel trick and propose an iterative method to solve the kernel regression problem, local reweighted multiple kernel regression (LR-MKR). The new framework of kernel learning approach includes two parts. First, an improved Nadaraya-Watson estimator based on blockwised approach is constructed to organize a data-driven localized reweighted criteria; Second, an iterative kernel learning method is introduced in a series decreased active set. Experiments on simulated and real data sets demonstrate the proposed method can avoid under fitting and over fitting simultaneously and improve the performance relative to the boundary effetely.