Estimation of high-dimensional change-points under a group sparsity structure

TL;DR

This paper introduces 'groupInspect', a new method for detecting change-points in high-dimensional data streams with group structures, providing theoretical guarantees and demonstrating strong empirical performance.

Contribution

The paper proposes a novel change-point detection procedure that exploits group sparsity, with proven minimax optimality and convergence guarantees, advancing high-dimensional change-point analysis.

Findings

The method achieves near-minimax optimal detection rates.

It performs competitively across various simulated scenarios.

Real data analysis confirms practical effectiveness.

Abstract

Change-points are a routine feature of 'big data' observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of all groups. We propose a new change point procedure, called 'groupInspect', that exploits the group sparsity structure to estimate a projection direction so as to aggregate information across the component series to successfully estimate the change-point in the mean structure of the series. We prove that the estimated projection direction is minimax optimal, up to logarithmic factors, when all group sizes are of comparable order. Moreover, our theory provide strong guarantees on the rate of convergence of the change-point location estimator. Numerical studies demonstrates the competitive performance of groupInspect in a wide range of settings and a real data example confirms the practical usefulness of our procedure.