A New Algrithm Designed For Weighted Samples Classification And Some New Boosting Algrithms Designed For Classification Based On Additive Logistic Regression Model

The Bagging method is an ensemble mecha.nism designed based entirely on reducing va.riance.Although this method performs well in classification problems,it has obvious disa.dvantages in reducing model bias.Since then,more and more statisticians have begun to design ensemble mechanisms of reducing the bias and variance,resulting in many Boosting algorithms such as DiscreteAdaBoost,RealAd-a.Boost.These algorithms have received extensive attention from statisticians due to their excellent performance.Many statisticians have begun t.o try explaining the statistical principles of the Boosting algorithm.After Friedman et al.attempted to use the additive logistic regression model to explain the reasons of the success of the Boosting algorithm,more and more Boosting algorithms were proposed.The Boost-ing algorithm trains weighted samples.Specifically,it sequentially trains classifiers for the weighted samples,and then ensembles these classifiers into a comprehensive classifier through a certain mechanism.For the classification problems,this paper improved the decision mechanism of Cart tree and proposed a logic tree model.Be-sides,based on the idea of ensemble learning,this paper proposed two new Boosting algorithms.This paper first discussed the principles of existing classifiers for weighted sam-ples,and proposed alogic tree model based on the idea of??quantile logistic regres-sion.This model makes better use the weight information of samples for weighted sample classification problems.Then,this paper analyzed the existing Boosting algorithms and proposed a more smoothing loss function,based on which two new Boosting algorithms were proposed.The new Boosting algorithms can avoid the over-fitting problem well,and the model has better robustness than the exponential loss because of the linear growth of the weight distribution of the error samples.Both the simulation and the application show that the proposed logic tree model can better adapt to the classification problem with the covariates of 10 to 50;the Boosting algorithm programs proposed in this paper is better than the existed Boost-ing algorithms in application.Furthermore,this paper extended the two proposed Boosting algorithms to the multi-classification problem based on the AdaBoost.MH idea.