Error analysis for l q -coefficient regularized moving least-square regression.

Abstract

We consider the moving least-square (MLS) method by the coefficient-based regression framework with $l^q$ -regularizer $(1\le q\le 2)$ and the sample dependent hypothesis spaces. The data dependent characteristic of the new algorithm provides flexibility and adaptivity for MLS. We carry out a rigorous error analysis by using the stepping stone technique in the error decomposition. The concentration technique with the $l^2$ -empirical covering number is also employed in our study to improve the sample error. We derive the satisfactory learning rate that can be arbitrarily close to the best rate $O\left(m^{-1}\right)$ under more natural and much simpler conditions.