A stochastic extended Rippa’s algorithm for LpOCV

L. Ling; F. Marchetti

doi:10.1016/j.aml.2022.107955

A stochastic extended Rippa’s algorithm for LpOCV

L. Ling, F. Marchetti^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

20 Citations (Scopus)

Abstract

In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm Rippa (1999) [1] has been extended to a more general cross validation setting. In this work, we propose a modification of such extension with the aim of further reducing the computational costs. The resulting Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested by means of various numerical experiments, which show its efficacy and effectiveness in different approximation settings.

Original language	English
Article number	107955
Journal	Applied Mathematics Letters
Volume	129
DOIs	https://doi.org/10.1016/j.aml.2022.107955
Publication status	Published - Jul 2022

Scopus Subject Areas

Applied Mathematics

User-Defined Keywords

Cross validation
Extended Rippa's Algorithm
RBF interpolation
Stochastic low-rank approximation

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10.1016/j.aml.2022.107955

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title = "A stochastic extended Rippa{\textquoteright}s algorithm for LpOCV",

abstract = "In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm Rippa (1999) [1] has been extended to a more general cross validation setting. In this work, we propose a modification of such extension with the aim of further reducing the computational costs. The resulting Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested by means of various numerical experiments, which show its efficacy and effectiveness in different approximation settings.",

keywords = "Cross validation, Extended Rippa's Algorithm, RBF interpolation, Stochastic low-rank approximation",

author = "L. Ling and F. Marchetti",

note = "Funding Information: This research has been accomplished with the financial support of GNCS-INAM and partially funded by the ASI-INAF grant “Artificial Intelligence for the analysis of solar FLARES data (AI-FLARES)”and the Hong Kong Research Grant Council GRF Grants. Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",

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journal = "Applied Mathematics Letters",

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T1 - A stochastic extended Rippa’s algorithm for LpOCV

AU - Ling, L.

AU - Marchetti, F.

N1 - Funding Information: This research has been accomplished with the financial support of GNCS-INAM and partially funded by the ASI-INAF grant “Artificial Intelligence for the analysis of solar FLARES data (AI-FLARES)”and the Hong Kong Research Grant Council GRF Grants. Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/7

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N2 - In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm Rippa (1999) [1] has been extended to a more general cross validation setting. In this work, we propose a modification of such extension with the aim of further reducing the computational costs. The resulting Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested by means of various numerical experiments, which show its efficacy and effectiveness in different approximation settings.

AB - In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm Rippa (1999) [1] has been extended to a more general cross validation setting. In this work, we propose a modification of such extension with the aim of further reducing the computational costs. The resulting Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested by means of various numerical experiments, which show its efficacy and effectiveness in different approximation settings.

KW - Cross validation

KW - Extended Rippa's Algorithm

KW - RBF interpolation

KW - Stochastic low-rank approximation

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DO - 10.1016/j.aml.2022.107955

M3 - Journal article

SN - 0893-9659

VL - 129

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 107955

ER -

A stochastic extended Rippa’s algorithm for LpOCV

Abstract

Scopus Subject Areas

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