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2020

Kernel Interpolation of High Dimensional Scattered Data

Lin, Shao-Bo, Chang, Xiangyu, Sun, Xingping

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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.
Incorporating a recently-developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high dimensional data, which features bounding stochastic approximation error by the spectrum of the underlying kernel matrix.

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