Multiple Change Points Detection in High-Dimensional Multivariate Regression

• Published in: Journal of systems science and complexity Vol. 35; no. 6; pp. 2278 - 2301
• Main Authors: Ma, Xiaoyan, Zhou, Qin, Zi, Xuemin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Complex Systems; Control; Dynamic programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Parameter estimation; Statistics; Systems Theory; dynamic programming; multi-task learning; low-rank structure; nuclear norm; Consistency
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-022-1205-6

This paper considers the problem of detecting structural changes in a high-dimensional regression setting. The structural parameters are subject to abrupt changes of unknown magnitudes at unknown locations. The authors propose a new procedure that minimizes a penalized least-squares loss function via a dynamic programming algorithm for estimating the locations of change points. To alleviate the computational burden, the authors adopt a prescreening procedure by eliminating a large number of irrelevant points before implementing estimation procedure. The number of change points is determined via Schwarz’s information criterion. Under mild assumptions, the authors establish the consistency of the proposed estimators, and further provide error bounds for estimated parameters which achieve almost-optimal rate. Simulation studies show that the proposed method performs reasonably well in terms of estimation accuracy, and a real data example is used for illustration.