# Kernel Interpolation of High Dimensional Scattered Data

arXiv: https://arxiv.org/abs/2009.01514 · HTML: https://mlsanity.com/paper/2009.01514/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay](https://mlsanity.com/paper/2309.13337/) (2023)
- [Generalization Performance of Empirical Risk Minimization on Over-parameterized Deep ReLU Nets](https://mlsanity.com/paper/2111.14039/) (2021)
- [Distributed Uncertainty Quantification of Kernel Interpolation on Spheres](https://mlsanity.com/paper/2310.16384/) (2023)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)
- [A Kernel Perspective on Distillation-based Collaborative Learning](https://mlsanity.com/paper/2410.17592/) (2024)
- [Sobolev norm inconsistency of kernel interpolation](https://mlsanity.com/paper/2504.20617/) (2025)

## Abstract (arXiv)

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. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high dimensional data.