Bayesian optimal change point detection in high-dimensions

TL;DR

This paper introduces Bayesian methods for detecting change points in high-dimensional data, focusing on mean and covariance changes, with proven consistency, near-optimal localization, and demonstrated effectiveness in simulations and real datasets.

Contribution

The paper presents the first Bayesian approach for high-dimensional change point detection using pairwise Bayes factors, with theoretical guarantees and practical validation.

Findings

Methods are consistent under mild conditions

Localization rates are nearly optimal

Effective in real-world genetic and financial data

Abstract

We propose the first Bayesian methods for detecting change points in high-dimensional mean and covariance structures. These methods are constructed using pairwise Bayes factors, leveraging modularization to identify significant changes in individual components efficiently. We establish that the proposed methods consistently detect and estimate change points under much milder conditions than existing approaches in the literature. Additionally, we demonstrate that their localization rates are nearly optimal in terms of rates. The practical performance of the proposed methods is evaluated through extensive simulation studies, where they are compared to state-of-the-art techniques. The results show comparable or superior performance across most scenarios. Notably, the methods effectively detect change points whenever signals of sufficient magnitude are present, irrespective of the number of signals. Finally, we apply the proposed methods to genetic and financial datasets, illustrating their practical utility in real-world applications.