Error analysis of the moving least-squares regression learning algorithm with β-mixing and non-identical sampling

Abstract

We consider the regression learning based on the moving least-squares framework for the polynomially β-mixing samples. The rigorous error analysis is carried out by using the independent-blocks technique in the sample error estimates. We derive the satisfactory learning rate that can be arbitrarily close to the best rate $O(m^{-1})$, when the sequence of marginal distributions converges exponentially to some marginal distribution in the dual of a Hölder space.

Keywords:

• Moving least-squares method
• weight function
• non-identical sampling
• mixing sequence
• total error
• learning rate

2010 AMS Subject Classifications:

• 68T05
• 68Q32
• 62J02

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the Natural Science Foundation of China (Grant No. 11671213).