High-dimensional sparsity-adaptive multiple change-point detection

2026-07-23

AI Summary

This study addresses the challenge of change-point detection in high-dimensional time series when the sparsity level of change points is unknown. The authors propose the first bottom-up framework for multiple change-point detection, which starts from the finest possible segmentation and iteratively merges adjacent segments. By integrating a test statistic that combines L2 and L∞ norms with its rank-based information, the method adaptively identifies change points under varying degrees of sparsity. Theoretical analysis establishes consistency in both the estimated number and locations of change points. Extensive simulations under independent Gaussian, dependent, and non-Gaussian noise settings, along with an empirical application to UK house price indices, demonstrate the superior performance and practical utility of the proposed approach compared to conventional top-down methods.

Abstract

We introduce a method for detecting multiple change-points in the mean of a high-dimensional data sequence. Unlike existing top-down (i.e. divisive) algorithms, we adopt a bottom-up (i.e. agglomerative) approach, whereby we iteratively merge neighboring segments of data starting from the finest level. This is particularly useful for signals with frequent change-points, since local evidence is assessed before segments are combined into coarser summaries. We compute $L_2$- and $L_\infty$-aggregated test statistics of neighboring segments and combine the information from their respective ranks, which makes the method adaptive in handling different degrees of change-point sparsity. We show the consistency of the estimated number and locations of change-points under both iid Gaussian and possibly dependent and/or non-Gaussian noise. The practicality of our approach is demonstrated through simulations and a real data example involving the UK House Price Index data.

Problem

• change-point detection
• high-dimensional data
• sparsity
• multiple change-points
• mean shift

Innovation

• change-point detection
• high-dimensional data
• bottom-up agglomeration
• sparsity-adaptive
• aggregated test statistics