Radial Basis Function Approximation with Distributively Stored Data on Spheres
This work addresses distributed learning for spherical data approximation, offering a theoretical guarantee for exploiting distributed data without access to all data, though it appears incremental in extending existing methods to this domain.
The paper tackled the problem of approximating spherical data stored across distributed servers without sharing, proposing a distributed weighted regularized least squares algorithm (DWRLS) that achieves optimal approximation rates and performs similarly to centralized methods.
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.