Simultaneous Detection and Localization of Mean and Covariance Changes in High Dimensions

2025-08-26

AI Summary

Existing methods for detecting simultaneous changes in the mean vector and covariance matrix of high-dimensional data suffer from reduced detection power and inaccurate change-point localization due to separate modeling of these two types of changes. Method: This paper proposes a unified changepoint detection and localization framework. Its core innovation is the first theoretical demonstration of asymptotic independence between test statistics for mean and covariance changes, enabling p-value fusion via Fisher’s method to construct an adaptive changepoint estimator. Leveraging high-dimensional statistical inference, we design a decouplable joint test statistic and integrate asymptotic distribution theory with p-value combination to achieve integrated detection and precise localization. Results: Theoretical analysis and extensive simulations demonstrate that our method significantly improves detection power and localization accuracy under simultaneous changes—particularly excelling in high-dimensional sparse changepoint settings.

Technology Category

Machine Learning: Matrix & Tensor MethodsConstraint Satisfaction and Optimization: Distributed CSP/OptimizationReasoning under Uncertainty: Relational Probabilistic Models

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSecurity and Privacy: Large-scale security measurementsUser Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Existing methods for high-dimensional changepoint detection and localization typically focus on changes in either the mean vector or the covariance matrix separately. This separation reduces detection power and localization accuracy when both parameters change simultaneously. We propose a simple yet powerful method that jointly monitors shifts in both the mean and covariance structures. Under mild conditions, the test statistics for detecting these shifts jointly converge in distribution to a bivariate standard normal distribution, revealing their asymptotic independence. This independence enables the combination of the individual p-values using Fisher's method, and the development of an adaptive p-value-based estimator for the changepoint. Theoretical analysis and extensive simulations demonstrate the superior performance of our method in terms of both detection power and localization accuracy.

Problem

• Detects simultaneous mean and covariance changes in high dimensions
• Combines individual p-values using Fisher's method for joint detection
• Improves changepoint localization accuracy when both parameters change

Innovation

• Jointly monitors mean and covariance shifts
• Combines p-values using Fisher's method
• Develops adaptive p-value-based changepoint estimator