Adaptable High-Dimensional Change Point Detection via Ridge Regularization
Abstract
We study the problem of detecting multiple change points in the mean vectors of an independent sequence of high-dimensional observations. Targeting at detecting dense alternatives in the regime where the dimension is comparable to the sample size, we propose a family of ridge-regularized CUSUM statistics built upon the adaptable ridge-regularized Hotelling's T2 test of Li et al. (Ann. Statist. 48 (2020) 1815--1847). Ridge regularization provides stable covariance normalization while allowing the tests to adapt to the underlying population covariance structure. To accommodate multiple change points without prior knowledge of their number or locations, we scan over a multi-scale collection of adjacent segments. We further enhance adaptability by aggregating information across a collection of ridge regularization parameters through the maximum of the corresponding test statistics. Under mild conditions, we establish the limiting distributions of the proposed statistics under the null hypothesis and a class of local alternatives. Extensive simulation studies demonstrate their finite-sample performance.
Related
- Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions
- Multiple Change Point Detection in the Mean and Covariance of High-Dimensional Matrix Time Series
- Graph-Based Change-Point Detection for Partially Observed High-Dimensional Data
- High-Dimensional Change Point Analysis for Temporally Dependent Data
- Extreme change-point detection
BibTeX
@misc{li2026adaptable,
title = {{Adaptable High-Dimensional Change Point Detection via Ridge Regularization}},
author = {Haoran Li and Haotian Xu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.24838},
eprint = {2605.24838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24838},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adaptable High-Dimensional Change Point Detection via Ridge Regularization
AU - Haoran Li
AU - Haotian Xu
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.24838
UR - https://arxiv.org/abs/2605.24838
AB - We study the problem of detecting multiple change points in the mean vectors of an independent sequence of high-dimensional observations. Targeting at detecting dense alternatives in the regime where the dimension is comparable to the sample size, we propose a family of ridge-regularized CUSUM statistics built upon the adaptable ridge-regularized Hotelling's T^2 test of Li et al. (Ann. Statist. 48 (2020) 1815--1847). Ridge regularization provides stable covariance normalization while allowing the tests to adapt to the underlying population covariance structure. To accommodate multiple change points without prior knowledge of their number or locations, we scan over a multi-scale collection of adjacent segments. We further enhance adaptability by aggregating information across a collection of ridge regularization parameters through the maximum of the corresponding test statistics. Under mild conditions, we establish the limiting distributions of the proposed statistics under the null hypothesis and a class of local alternatives. Extensive simulation studies demonstrate their finite-sample performance.
ER -