Error analysis of the moving least-squares method with non-identical sampling

Abstract

ABSTRACTWe derive the convergence rate of the moving least-squares learning algorithm for regression under the assumption that the samples are drawn from a non-identical sequence of probability measures. The error analysis is carried out by analysing the drift error and using the probability inequalities for the non-identical sampling. When the sequence of marginal distributions converges exponentially to marginal distribution in the dual of a Hölder space, we obtain the satisfactory capacity dependent error bounds of the algorithm that can be arbitrarily close to the rate .