The Tractability of Gaussian Kernel Function Approximation with Nonhomogeneous Shape Parameter

The Gaussian kernel is a popular choice for radial basis function approximation. For a fixed dimension, the error decays exponentially with sample size. However, the leading coefficient of error is dimension dependent. If the shape parameter is nonhomogeneous, and the importance of the variables decays sufficiently fast with coordinate index, then the error can be shown to be uniformly bounded by a polynomial in the inverse of the sample size.

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Computational Mathematics & Statistics