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

ABSTRACT

We 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 $O\left(m^{-1}\right)$.

Keywords:

• Moving least-squares method
• non-identical sampling
• drift error
• Bernstein inequality
• learning rates

2010 AMS subject Classifications:

• 68T05
• 68Q32
• 62J02

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Qin Guo http://orcid.org/0000-0002-5355-5857

Additional information

Funding

The work is supported by the National Natural Science Foundation of China [Grant Nos. 11271199, 11671213].