# Distributed Uncertainty Quantification of Kernel Interpolation on Spheres

arXiv: https://arxiv.org/abs/2310.16384 · HTML: https://mlsanity.com/paper/2310.16384/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Distributed filtered hyperinterpolation for noisy data on the sphere](https://mlsanity.com/paper/1910.02434/) (2019)
- [Kernel Interpolation of High Dimensional Scattered Data](https://mlsanity.com/paper/2009.01514/) (2020)
- [Radial Basis Function Approximation with Distributively Stored Data on Spheres](https://mlsanity.com/paper/2112.02499/) (2021)

## Built on by (most cited first, 2 of 2)

- [Weighted Spectral Filters for Kernel Interpolation on Spheres: Estimates of Prediction Accuracy for Noisy Data](https://mlsanity.com/paper/2401.08364/) (2024)
- [Integral Operator Approaches for Scattered Data Fitting on Spheres](https://mlsanity.com/paper/2401.15294/) (2024)

## Abstract (arXiv)

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.