Distributed regularized least squares with flexible Gaussian kernels
Abstract We propose a distributed learning algorithm for least squares regression in reproducing kernel Hilbert spaces (RKHSs) generated by flexible Gaussian kernels, based on a divide and conquer strategy. Our study demonstrates that Gaussian kernels with flexible variances greatly improve the learning performance of distributed algorithms generated by a fixed Gaussian. Under some mild conditions, we establish sharp error bounds for the distributed algorithm with labeled data in which the variance of the Gaussian kernel serves as a tuning parameter. We show that with suitably chosen parameters our error rates can be almost mini max optimal under the standard Sobolev smoothness condition on the target function. By utilizing additional information of unlabeled data for semi supervised learning, we relax the restrictions on the number of data partition and the range of the Sobolev smoothness index.
Applied and Computational Harmonic Analysis