High-dimensional change-point detection with sparse alternatives

TL;DR

This paper introduces an adaptive test for detecting mean changes in high-dimensional Gaussian vectors, focusing on sparse changes in some components, and establishes its optimal detection boundary.

Contribution

It proposes a new adaptive change-point detection method for sparse signals in high dimensions and proves its rate-optimality under certain asymptotic conditions.

Findings

Detection boundary characterized for high-dimensional sparse changes

Proposed test is rate-optimal in the asymptotic regime

Method adapts to the number of changing components

Abstract

We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a change-point that is adaptive to the number of changing components. Under the assumption that the vector dimension tends to infinity and the length of the sequence grows slower than the dimension of the signal, we obtain the detection boundary for this problem and prove its rate-optimality.