Distributed Regression Learning With Coefficient Regularization

In recent years,the analysis of big data has become one of the hot research topics in many fields,such as statistics,mathematics,and computer science and so on.Actually,big data has two meanings:one is the large number of data;the other is a large number of unlabeled and messy data.Due to the large number of data,the ideas of parallel computing and distributed learning have been widely concerned in learning theory.The basic idea of distributed learning is to partition a large data set?z _i?^N_i?28?1into m disjoint parts in some way and send them to m data processors;each part is first processed separately to get an output function,and then takes an average of the individual output functions as a final global estimator.Because of the different purposes of data analysis,the algorithms of distributed learning are various.This paper mainly focuses on the mathematical foundation of distributed and coefficient based regularization regression learning.By the techniques of sampling operator and integral operator,and some new ideas about error decomposition,satisfied error bound and learning rates are deduced.Based on our research conclusions,when m does not exceed a certain threshold,this distributed learning has the same convergence rate compared with the algorithm processing the whole data in one single machine.The main contents of this article are divided into:In Chapter one,the development history and basic framework of statistical learning theory are introduced.In Chapter two,the research background and preparatory knowledges of the regularized learning are introduced,and focuses on the research status of the coefficient regularized learning.In Chapter three,the research status of distributed learning problem is introduced,and this chapter mainly introduced the distributed learning with kernel ridge regression.In Chapter four,distributed regression learning with coefficient regularization is introduced,and this chapter mainly studied the distributed regression learning with coefficient regularization and distributed learning with partial coefficients regularization.By using the techniques of sampling operator and integral operator,and a decomposition of operator differences,error bounds and learning rates of the two algorithms are obtained.In Chapter five,the summary and prospect are introduced.