Radial Basis Function Approximation with Distributively Stored Data on Spheres

2021/12/05 by Feng Han, Feng, Han, Shao-Bo Lin +3
Engineering · Environmental Science · #Advanced Adaptive Filtering Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Urban Heat Island Mitigation

paper · pdf · doi:10.48550/arxiv.2112.02499

openalex publication_date 2021/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Distributed learning with regularized least squares
• An Optimization Approach to Weight Collocation for Scattered Spherical Data
• Distributed Uncertainty Quantification of Kernel Interpolation on Spheres
• Distributed Principal Component Analysis with Limited Communication
• Stable and accurate least squares radial basis function approximations on bounded domains