# Distributed filtered hyperinterpolation for noisy data on the sphere

arXiv: https://arxiv.org/abs/1910.02434 · HTML: https://mlsanity.com/paper/1910.02434/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Radial Basis Function Approximation with Distributively Stored Data on Spheres](https://mlsanity.com/paper/2112.02499/) (2021)
- [Distributed Gradient Descent for Functional Learning](https://mlsanity.com/paper/2305.07408/) (2023)
- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)
- [Distributed Uncertainty Quantification of Kernel Interpolation on Spheres](https://mlsanity.com/paper/2310.16384/) (2023)
- [Weighted Spectral Filters for Kernel Interpolation on Spheres: Estimates of Prediction Accuracy for Noisy Data](https://mlsanity.com/paper/2401.08364/) (2024)
- [Sketching with Spherical Designs for Noisy Data Fitting on Spheres](https://mlsanity.com/paper/2303.04550/) (2023)
- [Theory of Decentralized Robust Kernel-Based Learning](https://mlsanity.com/paper/2506.05215/) (2025)

## Abstract (arXiv)

Problems in astrophysics, space weather research and geophysics usually need to analyze noisy big data on the sphere. This paper develops distributed filtered hyperinterpolation for noisy data on the sphere, which assigns the data fitting task to multiple servers to find a good approximation of the mapping of input and output data. For each server, the approximation is a filtered hyperinterpolation on the sphere by a small proportion of quadrature nodes. The distributed strategy allows parallel computing for data processing and model selection and thus reduces computational cost for each server while preserves the approximation capability compared to the filtered hyperinterpolation. We prove quantitative relation between the approximation capability of distributed filtered hyperinterpolation and the numbers of input data and servers. Numerical examples show the efficiency and accuracy of the proposed method.