Coefficient-based Regularization Network With Variance Loss For Error

Generally,the kernel based learning algorithm does not add the bias term.However,for linear learning systems,such as linear support vector machine,linear canonical correlation analysis,linear regression learning and regression learning based on spline curve,adding the bias term can improve the approximation ability of linear function hypothesis space.Of course,if the reproducing kernel Hilbert spaceH_K is large enough to approximate any continuous function,the shift term seems to be redundant in theory.It is generally believed that the offset term can indeed improve the performance of the learning algorithm,but at the same time it also brings essential difficulties to the theoretical analysis of the algorithm.In2018,Wang Chendi and Guo Xin adopted the connection between the regularization algorithm of kernel ridge regression with offset term and the center reproducing kernel,proved the extended error bound of kernel ridge regression with offset term,and obtained the satisfactory learning rate of the algorithm.In this paper,the regularization algorithm based on variance loss is introduced for the learning algorithm of coefficient regularization regression with offset term.The kernel function in this algorithm does not need to be symmetric positive definite,but only continuous,bounded and weak capacity conditions.In this paper,the analytic expression of the objective function or optimization function in the learning algorithm is obtained from the approximation error.The error is further decomposed into approximation error,sample error and assumed space error.The error of the three parts is estimated by different methods.Finally,the learning rate of the algorithm is obtained by iteration.The content of this paper is divided into the following chapters:The first chapter introduces the current situation and basic framework of the research on machine learning and statistical learning theory.In chapter two,we first introduce the Hilbert space and related operators of the regeneration core,and then introduce the regularization algorithm,including regularization least square algorithm,coefficient regularization algorithm and regularization regression learning algorithm with offset term.In chapter three,the algorithm of this paper is introduced,which is coefficient regularization regression learning based on variance loss.Firstly,the background of the study is introduced.Secondly,the assumption conditions and main results of this chapter are introduced.Then,the error analysis framework is introduced,including approximation error,assumed space error and sample error.Finally,the error boundary and learning rate are calculated by iterative method.Chapter four summarizes the main research results of this paper and proposes the next work plan.