Applications Of Decomposition Algorithms And Quantile Regression

This paper has studied various decomposition algorithms and their applications based on support vector machine models.We have trained benchmark data sets by SVM^Lightand SMO algorithm,and compared the simulation results generated by dif-ferent kernel functions.In addition,we have discussed how to choose suitable kernel functions in different optimization problems.Quantile regression is an important topic in statistics and machine learning.This work has investigated online quantile regression algorithm associated with Gaussian kernels in the setting of non-identical sampling.By introducing?-insensitive pinball losses and dual H¨older space in non-identical distri-butions,we have derived the convergence rate of online quantile regression algorithm.Mathematical analysis depends on the error decomposition and the iteration method.Specially,taking the median regression as an example,we have investigated the effects of parameters in keeping sparsity and nice learning power for quantile problems.Our result can be extended to general quantile regression problems.