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Adaptive Matrix Change Point Detection: Leveraging Structured Mean Shifts
Preprint   Open access

Adaptive Matrix Change Point Detection: Leveraging Structured Mean Shifts

Xinyu Zhang and Kung-Sik Chan
arXiv.org
Cornell University
01/30/2024
DOI: 10.48550/arxiv.2401.17473
url
https://doi.org/10.48550/arXiv.2401.17473View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that are activated by a change may cluster along certain rows (columns), which forms mode-specific change point alignment. Leveraging mode-specific change point alignments may substantially enhance the power for change point detection. Yet, there may be no mode-specific alignments in the change point structure. We propose a powerful test to detect mode-specific change points, yet robust to non-mode-specific changes. We show the validity of using the multiplier bootstrap to compute the p-value of the proposed methods, and derive non-asymptotic bounds on the size and power of the tests. We also propose a parallel bootstrap, a computationally efficient approach for computing the p-value of the proposed adaptive test. In particular, we show the consistency of the proposed test, under mild regularity conditions. To obtain the theoretical results, we derive new, sharp bounds on Gaussian approximation and multiplier bootstrap approximation, which are of independent interest for high dimensional problems with diverging sparsity.
 Mathematics - Statistics Theory Statistics - Methodology Statistics - Theory

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