Low-Rank Matrix Estimation in the Presence of Change-Points
Lei Shi, Guanghui Wang, Changliang Zou.
Year: 2024, Volume: 25, Issue: 220, Pages: 1−71
Abstract
We consider a general trace regression model with multiple structural changes and propose a universal approach for simultaneous exact or near-low-rank matrix recovery and change-point detection. It incorporates nuclear norm penalized least-squares minimization into a grid search scheme that determines the potential structural break. Under a set of general conditions, we establish the non-asymptotic error bounds with a nearly-oracle rate for the matrix estimators as well as the super-consistency rate for the change-point localization. We use concrete random design instances to justify the appropriateness of the proposed conditions. Numerical results demonstrate the validity and effectiveness of the proposed scheme.