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arXiv · 2607.20928

High-dimensional sparsity-adaptive multiple change-point detection

Hyeyoung Maeng·Tengyao Wang·Piotr Fryzlewicz
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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.

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Hyeyoung Maeng, Tengyao Wang, Piotr Fryzlewicz. 2026-07-23. High-dimensional sparsity-adaptive multiple change-point detection. https://arxiv.org/abs/2607.20928

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