| Abstract: |
| Data sites selected from modeling high-dimensional problems often appear scattered in
non-paternalistic ways. Except for sporadic-clustering at some spots, they become relatively
far apart as the dimension of the ambient space grows. These features defy any theoretical
treatment that requires local or global quasi-uniformity of distribution of data sites. Incor-
porating a recently-developed application of integral operator theory in machine learning,
we propose and study a new framework to analyze kernel interpolation of high dimensional
data in the current article, which features bounding stochastic approximation error by the
spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simula-
tions show that spectra of kernel matrices are reliable and stable barometers for gauging the
performance of kernel-interpolation methods for high dimensional data. |
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