## Learning Theory of Distributed Regression with Bias Corrected Regularization Kernel Network

*Zheng-Chu Guo, Lei Shi, Qiang Wu*; 18(118):1−25, 2017.

### 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.

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