Title: Learning Theory of Distributed Regression with Bias Corrected Regularization Kernel Network,
Abstract: Distributed learning is an effective way to analyze big data. In distributed
regression, a typical approach is to divide the big data into multiple blocks,
apply a base regression algorithm on each of them, and then simply average the
output functions learnt from these blocks. Since the average process will
decrease the variance, not the bias, bias correction is expected to improve the
learning performance if the base regression algorithm is a biased one.
Regularization kernel network is an effective and widely used method for
nonlinear regression analysis. In this paper we will investigate a bias
corrected version of regularization kernel network. We derive the error bounds
when it is applied to a single data set and when it is applied as a base
algorithm in distributed regression. We show that, under certain appropriate
conditions, the optimal learning rates can be reached in both situations.