Change-point detection in variance-covariance matrix
Abstract
We consider the joint estimation of change-point locations and the sparsity pattern of the variance-covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change-point detection and covariance estimation accuracy. We establish the conditions under which the estimated change points and the sparse estimators within each segment are consistent. To solve the resulting optimization problem efficiently, we develop an alternating direction method of multipliers (ADMM) whose updates reduce to computationally tractable subproblems. The performance of the proposed method is illustrated through synthetic and real-data experiments, including comparisons with several competing procedures.
Related
- Multiple Change Point Detection in the Mean and Covariance of High-Dimensional Matrix Time Series
- Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond
- Bootstrap-Calibrated Spectral Divergence Tests for Online Detection of Covariance Matrix Changes
- Extreme change-point detection
- Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions
BibTeX
@misc{lin2026changepoint,
title = {{Change-point detection in variance-covariance matrix}},
author = {Ying Lin and Benjamin Poignard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.12881},
eprint = {2605.12881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12881},
}
RIS
TY - UNPB
TI - Change-point detection in variance-covariance matrix
AU - Ying Lin
AU - Benjamin Poignard
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.12881
UR - https://arxiv.org/abs/2605.12881
AB - We consider the joint estimation of change-point locations and the sparsity pattern of the variance-covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change-point detection and covariance estimation accuracy. We establish the conditions under which the estimated change points and the sparse estimators within each segment are consistent. To solve the resulting optimization problem efficiently, we develop an alternating direction method of multipliers (ADMM) whose updates reduce to computationally tractable subproblems. The performance of the proposed method is illustrated through synthetic and real-data experiments, including comparisons with several competing procedures.
ER -