Moving least-square method in learning theory

Hong-Yan Wang; Dao-Hong Xiang; Ding-Xuan Zhou

doi:10.1016/j.jat.2009.12.002

Moving least-square method in learning theory

Hong-Yan Wang
, Dao-Hong Xiang
, Ding-Xuan Zhou

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

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 L² error measuring the global approximation on the whole domain are provided. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	599-614
Journal	Journal of Approximation Theory
Volume	162
Issue number	3
DOIs	https://doi.org/10.1016/j.jat.2009.12.002
Publication status	Published - Mar 2010

Research Keywords

Approximation error
Learning theory
Moving least-square method
Norming condition
Sample error

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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 L2 error measuring the global approximation on the whole domain are provided. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

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T1 - Moving least-square method in learning theory

AU - Wang, Hong-Yan

AU - Xiang, Dao-Hong

AU - Zhou, Ding-Xuan

PY - 2010/3

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N2 - 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 L2 error measuring the global approximation on the whole domain are provided. © 2009 Elsevier Inc. All rights reserved.

AB - 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 L2 error measuring the global approximation on the whole domain are provided. © 2009 Elsevier Inc. All rights reserved.

KW - Approximation error

KW - Learning theory

KW - Moving least-square method

KW - Norming condition

KW - Sample error

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U2 - 10.1016/j.jat.2009.12.002

DO - 10.1016/j.jat.2009.12.002

M3 - RGC 21 - Publication in refereed journal

SN - 0021-9045

VL - 162

SP - 599

EP - 614

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 3

ER -

Moving least-square method in learning theory

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Research Keywords

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