Multivariate change point detection for heterogeneous series

Abstract

The multivariate change point detection problem has been encountered across various fields. Most approaches to this problem assume the series is homogeneous, i.e., all the coordinates change concurrently. Hence, the specific subset of the coordinates containing the change points cannot be determined. In this work, we propose S-MCPD, which is capable of detecting the position of multivariate change points for heterogeneous series by identifying specific coordinates of those changed. Specifically, the problem is discussed in the context of variable selection and transformed into the form of sparse group lasso. In simulation studies, we compared S-MCPD with four existing methods, inspect, sbs, dc, and cpm. The results showed that the performance of S-MCPD was comparable to that of inspect and was superior to other methods in terms of evaluation metrics. In addition, S-MCPD can determine not only the positions of change points, but also the subset of coordinates containing the change points, while other existing methods are unable to achieve this. Moreover, S-MCPD does not depend on the constant variance assumption and works quite well even when the covariance changes, which makes our method more practical. These are the two important contributions of our work. Finally, we applied S-MCPD to two real-world datasets to show its effectiveness.