Covariate-Assisted Matrix Completion with Multiple Structural Breaks

作     者：MENG Jing FENG Long ZOU Changliang WANG Zhaojun MENG Jing;FENG Long;ZOU Changliang;WANG Zhaojun

作者机构：School of Statistics and Data ScienceKLMDASRLEBPSand LPMCNankai UniversityTianjin 300071China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2024年第37卷第2期

页      面：692-728页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12226007,12271271,11925106,12231011,11931001 and 11971247 the Fundamental Research Funds for the Central Universities under Grant No.ZB22000105 the China National Key R&D Program under Grant Nos.2022YFA1003703,2022YFA1003800,and 2019YFC1908502 

主　　题：Additional covariates matrix completion multiple structural breaks wild Binary Segmentation 

摘      要：In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix *** this paper,the authors consider the matrix recovery problem when there are multiple structural breaks in the coefficient matrix β under the column-space-decomposition model A=Xβ+B.A cumulative sum(CUSUM)statistic is constructed based on the penalized estimation of β.Then the CUSUM is incorporated into the Wild Binary Segmentation(WBS)algorithm to consistently estimate the location of ***,a nearly-optimal recovery of A is *** findings are further corroborated via numerical experiments and a real-data application.