带变点的混合模型的统计推断与算法设计

Statistical Inference and Algorithm Design of Mixture Model with Change Point

本文研究了带变点的混合模型中的统计推断与算法设计问题.针对存在变点的多分类混合数据,本文基于参数的极大似然估计设计了一种改进的EM算法,并证明了变点估计量和混合参数估计量的大样本性质.为了验证方法的有效性,我们进行了模拟实验,结果表明:不考虑变点的EM算法对于分类结果估计较差,甚至会丢掉一些类别;我们改进的EM算法能够精确地定位出变点位置,同时对于每个类别的相应参数均获得准确的估计.

This paper studies the statistical inference and algorithm design problems in the mixture model with change point.For multi-classified mixture data with change point,this paper designs an improved EM algorithm based on the maximum likelihood estimation of parameters,and proves the large sample nature of the change point estimator and the mixture parameter estimator.In order to verify the effectiveness of the method,we conducted some simulation experiments.The results show that the EM algorithm that does not consider the change point has a poor estimate on the classification result,and even loses some categories;Our improved EM algorithm can accurately locate the location of the change point,and at the same time obtain accurate estimates for the corresponding parameters of each category.