Posterior contraction rate of sparse latent feature models with application to proteomics

作     者：Tong Li Tianjian Zhou Kam-Wah Tsui Lin Wei Yuan Jie Tong Li;Tianjian Zhou;Kam-Wah Tsui;Lin Wei;Yuan Ji

作者机构：Department of StatisticsColumbia UniversityNew YorkNYUSA Department of StatisticsColorado State UniversityFort CollinsCOUSA Department of StatisticsUniversity of Wisconsin-MadisonMadisonWIUSA Research InstituteNorthShore University HealthSystemEvanstonILUSA Department of Public Health SciencesUniversity of ChicagoChicagoILUSA 

出 版 物：《Statistical Theory and Related Fields》 (统计理论及其应用（英文）)

年 卷 期：2022年第6卷第1期

页      面：29-39页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：High dimension indian buffet process latent feature Markov chain monte carlo posterior convergence reverse phase protein arrays 

摘      要：The Indian buffet process(IBP)and phylogenetic Indian buffet process(pIBP)can be used as prior models to infer latent features in a data *** theoretical properties of these models are under-explored,however,especially in high dimensional *** this paper,we show that under mild sparsity condition,the posterior distribution of the latent feature matrix,generated via IBP or pIBP priors,converges to the true latent feature matrix *** derive the posterior convergence rate,referred to as the contraction *** show that the convergence results remain valid even when the dimensionality of the latent feature matrix increases with the sample size,therefore making the posterior inference valid in high dimensional *** demonstrate the theoretical results using computer simulation,in which the parallel-tempering Markov chain Monte Carlo method is applied to overcome computational *** practical utility of the derived properties is demonstrated by inferring the latent features in a reverse phase protein arrays(RPPA)dataset under the IBP prior model.