# Sketching with Spherical Designs for Noisy Data Fitting on Spheres

arXiv: https://arxiv.org/abs/2303.04550 · HTML: https://mlsanity.com/paper/2303.04550/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 9 of 9)

- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [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)
- [Analysis of regularized Nystr"om subsampling for regression functions of low smoothness](https://mlsanity.com/paper/1806.00826/) (2018)
- [Distributed filtered hyperinterpolation for noisy data on the sphere](https://mlsanity.com/paper/1910.02434/) (2019)
- [Radial Basis Function Approximation with Distributively Stored Data on Spheres](https://mlsanity.com/paper/2112.02499/) (2021)
- [Nystr"om Regularization for Time Series Forecasting](https://mlsanity.com/paper/2111.07109/) (2021)

## Built on by (most cited first, 1 of 1)

- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)

## Abstract (arXiv)

This paper proposes a sketching strategy based on spherical designs, which is applied to the classical spherical basis function approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to demonstrate the feasibility of the proposed { sketching} strategy. From the theoretical side, we prove that sketching based on spherical designs can reduce the computational burden of the spherical basis function approach without sacrificing its approximation capability. In particular, we provide upper and lower bounds for the proposed { sketching} strategy to fit noisy data on spheres. From the experimental side, we numerically illustrate the feasibility of the sketching strategy by showing its comparable fitting performance with the spherical basis function approach. These interesting findings show that the proposed sketching strategy is capable of fitting massive and noisy data on spheres.