Convergence Analysis Of Online Regression Learning With Kernel Regularization Based On RRKH

Regularization regression learning is one of the important research fields of statistical learning theory,which has been widely used in real life.The purpose of regression learning is to mine the statistical laws behind the data,study the error bound and learning rate of the regularization regression learning algorithm,so as to prove the consistency of the algorithm and establish the corresponding mathematical foundation for the application of the algorithm,which has important theoretical and practical significance.Due to the inevitable measurement error,the point-evaluation function cannot be accurately measured,so the local mean value of the function is used as the observation information.In practice,many available data appear in the form of non-point-evaluation.The example of the integral function shows that the functional reproducing kernel Hilbert space(FRKHS)is a useful development of the classical reproducing kernel Hilbert space,which lays a functional analysis foundation for learning non-point-evaluation function data by using the kernel regularization method,and provides a good hypothesis space for studying non-point-evaluation function data modeling.Therefore,It is of great significance to extend the research methods and theories of convergence analysis of kernel regularization online regression learning algorithm based on reproducing kernel Hilbert space to the framework of functional reproducing kernel Hilbert space,which is also a new research direction.Based on the convergence analysis of the existing kernel regularization online regression learning algorithm of reproducing kernel Hilbert space,this paper extends the space,gives a complete error analysis of the kernel regularization online learning algorithm related to the parameterized loss function,and obtains the error estimation and learning rate of the corresponding learning algorithm;The results show that the learning rate can be improved by properly adjusting the parameters in the parameterized loss function.In addition,as an auxiliary conclusion of the study,we give some specific examples of Radon reproducing kernel Hilbert spaces in different regions with the help of Fourier analysis constructor reproducing kernel Hilbert spaces,and give the corresponding reproducing kernel and perform convergence analysis.