Doubly stochastic radial basis function methods

Fenglian Yang*, Liang Yan, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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).

Original languageEnglish
Pages (from-to)87-97
Number of pages11
JournalJournal of Computational Physics
Volume363
DOIs
Publication statusPublished - 15 Jun 2018

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

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

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