Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

We propose a doubly stochastic radial basis function (DSRBF) method for function recoveries. Instead of a constant, we treat the RBF shape parameters as stochastic variables whose distribution were determined by a stochastic leave-one-out cross validation (LOOCV) estimation. A careful operation count is provided in order to determine the ranges of all the parameters in our methods. The overhead cost for setting up the proposed DSRBF method is O(n2) for function recovery problems with n basis. Numerical experiments confirm that the proposed method not only outperforms constant shape parameter formulation (in terms of accuracy with comparable computational cost) but also the optimal LOOCV formulation (in terms of both accuracy and computational cost).

Keywords

Kernel methods, Collocation, Function recovery, Stochastic LOOCV, Random shape parameters

Publication Date

6-2018

Source Publication Title

Journal of Computational Physics

Volume

363

Start Page

87

End Page

97

Publisher

Elsevier

DOI

10.1016/j.jcp.2018.02.042

Link to Publisher's Edition

https://doi.org/10.1016/j.jcp.2018.02.042

ISSN (print)

00219991

Available for download on Wednesday, July 01, 2020

Included in

Mathematics Commons

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