Distributed Uncertainty Quantification of Kernel Interpolation on Spheres
This addresses uncertainty quantification in kernel interpolation for noisy spherical data, which is an incremental improvement in a domain-specific context.
The paper tackles the problem of radial basis function kernel interpolation being susceptible to noisy data due to an uncertainty relation, proposing a distributed interpolation method to manage and quantify uncertainty for noisy spherical data, with numerical simulations showing it is practical and robust.
For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an "uncertainty relation", an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in terms of handling noisy data from challenging computing environments.