Research On Optimal Quantile Regression Based On Variable Gaussian Kernel Function

Support vector machines(SVMs)using Gaussian kernels are one of the standard and state-of-the-art learning algorithms.Gaussian kernels with flexible variances provide a rich family of Mercer kernels for learning algorithms.Because variable Gaussian kernel functions can provide a rich family of Mercer kernels,Of the re-generative kernel Hilbert space to study the problem of regression and classification in learning theory has become a hot spot in the recent study of statistical learning theory.This mainly benefits from choosing suitable Gaussian kernel variance param-eters according to different learning problems,we will get learning rates estimates of the regression and classification problems.The quantile regression problem is a very important class of problems in statistical learning theory.The usual research approach is to use a fixed Gaussian kernel function Corresponding Regeneration Kernel Considering the quantile regression problem in the Hilbert space,the limita-tion is that in choosing the regenerative kernel,the Hilbert space loses its flexibility.In this paper,In the reproducing kernel Hilbert space corresponding to the kernel function,the approximation algorithm of the quantile regression problem is given by choosing the appropriate variance parameter and using the Tikhonov regulariza-tion strategy And learning rate estimates.