Moving least-square method in learning theory

Authors:
Hong-Yan Wang;Dao-Hong Xiang;Ding-Xuan Zhou
Affiliations:
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310018, China;Department of Mathematics, Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China;Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
Venue:
Journal of Approximation Theory
Year:
2010

Citing 4
Cited 2

The approximation power of moving least-squares

Mathematics of Computation
Error estimates for scattered data interpolation on spheres

Mathematics of Computation
A two-dimensional interpolation function for irregularly-spaced data

ACM '68 Proceedings of the 1968 23rd ACM national conference
Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)

Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)

Full length article: Concentration estimates for the moving least-square method in learning theory

Journal of Approximation Theory
Statistical analysis of the moving least-squares method with unbounded sampling

Information Sciences: an International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

Moving least-square (MLS) is an approximation method for data interpolation, numerical analysis and statistics. In this paper we consider the MLS method in learning theory for the regression problem. Essential differences between MLS and other common learning algorithms are pointed out: lack of a natural uniform bound for estimators and the pointwise definition. The sample error is estimated in terms of the weight function and the finite dimensional hypothesis space. The approximation error is dealt with for two special cases for which convergence rates for the total L^2 error measuring the global approximation on the whole domain are provided.