In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix A.In this paper,the authors consider the matrix recovery proble...In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix A.In 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 breaks.Consequently,a nearly-optimal recovery of A is fulfilled.Theoretical findings are further corroborated via numerical experiments and a real-data application.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12226007,12271271,11925106,12231011,11931001 and 11971247the Fundamental Research Funds for the Central Universities under Grant No.ZB22000105the China National Key R&D Program under Grant Nos.2022YFA1003703,2022YFA1003800,and 2019YFC1908502.
文摘In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix A.In 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 breaks.Consequently,a nearly-optimal recovery of A is fulfilled.Theoretical findings are further corroborated via numerical experiments and a real-data application.
