# Radial Basis Function Approximation with Distributively Stored Data on Spheres

arXiv: https://arxiv.org/abs/2112.02499 · HTML: https://mlsanity.com/paper/2112.02499/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 56 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces](https://mlsanity.com/paper/1801.06720/) (2018)
- [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)
- [Divide and Conquer Local Average Regression](https://mlsanity.com/paper/1601.06239/) (2016)
- [Nonparametric regression using needlet kernels for spherical data](https://mlsanity.com/paper/1502.04168/) (2015)

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

- [Tractability of approximation by general shallow networks](https://mlsanity.com/paper/2308.03230/) (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)
- [Integral Operator Approaches for Scattered Data Fitting on Spheres](https://mlsanity.com/paper/2401.15294/) (2024)

## Abstract (arXiv)

This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical data that are stored across numerous local servers and cannot be shared with each other. Via developing a novel integral operator approach, we succeed in deriving optimal approximation rates for DWRLS and theoretically demonstrate that DWRLS performs similarly as running a weighted regularized least squares algorithm with the whole data on a large enough machine. This interesting finding implies that distributed learning is capable of sufficiently exploiting potential values of distributively stored spherical data, even though every local server cannot access all the data.