Department of Mathematics
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).
Kernel methods, Collocation, Function recovery, Stochastic LOOCV, Random shape parameters
Source Publication Title
Journal of Computational Physics
Link to Publisher's Edition
Yang, F., Yan, L., & Ling, L. (2018). Doubly stochastic radial basis function methods. Journal of Computational Physics, 363, 87-97. https://doi.org/10.1016/j.jcp.2018.02.042