基于Inspect投影的高维数据贝叶斯变点检验  

Bayesian Changepoint Test Method for High-Dimensional Data Based on Inspect Projection

作　　者：郭宇婷 施三支[1] 张欣[1] GUO Yuting;SHI Sanzhi;ZHANG Xin(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022)

机构地区：[1]长春理工大学数学与统计学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2024年第5期134-142,共9页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(11601039);吉林省教育厅项目(JJKH20210809KJ)。

摘　　要：高维数据的多变点检验已经成为了一个热点问题。针对高斯噪声下的高维数据,提出了一种基于Inspect投影的贝叶斯变点检验方法。该方法利用Inspect投影,通过奇异值分解(SVD)计算最优投影方向,沿该方向将高维数据投影到一维空间,并通过引入贝叶斯先验信息,对降维后的数据进行变点检验。通过数值模拟,该方法在样本量n,维度p,变点的稀疏度k的不同设置下的检验结果均优于Inspect方法。最后将该方法应用到膀胱肿瘤患者微阵列数据集(ACGH)中。Multiple changepoint detection in high-dimensional data has become a hot topic.This paper proposes a Bayesian changepoint detection method based on Inspect projection for high-dimensional data with Gaussian noise.This method utilizes Inspect projection to calculate the optimal projection direction through singular value decomposition(SVD),projects the high-dimensional data onto a one-dimensional space along this direction,and incorporates Bayesian prior information to perform changepoint detection on the dimension-reduced data.Numerical simulations show that this method outperforms the Inspect method under different settings of sample size n,dimension p,and changepoint sparsity k.Finally,this method is applied to the microarray dataset(ACGH)of bladder tumor patients.

关 键 词：高维数据 Inspect投影 贝叶斯 变点检验 

分 类 号：O212.1[理学—概率论与数理统计]