Covariate-Assisted Matrix Completion with Multiple Structural Breaks

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.