  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.
