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Doubly stochastic radial basis function methods
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DOI：10.1016/j.jcp.2018.02.042.png)
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Abstract
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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(n(2)) for function recovery problems with nbasis. 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). (C) 2018 Elsevier Inc. All rights reserved.
Keywords:
Kernel methods
Collocation
Function recovery
Stochastic LOOCV
Random shape parameters
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