Convergence rate for the moving least-squares learning with dependent sampling

J Inequal Appl. 2018;2018(1):200. doi: 10.1186/s13660-018-1794-8. Epub 2018 Jul 31.

Abstract

We consider the moving least-squares (MLS) method by the regression learning framework under the assumption that the sampling process satisfies the α-mixing condition. We conduct the rigorous error analysis by using the probability inequalities for the dependent samples in the error estimates. When the dependent samples satisfy an exponential α-mixing, we derive the satisfactory learning rate and error bound of the algorithm.

Keywords: Error bound; Mixing sequence; Moving least-squares; Probability inequality; Regression function.