Optimal multiple change-point detection for high-dimensional data

TL;DR

This paper introduces a versatile algorithm for detecting multiple change-points in high-dimensional data, demonstrating its effectiveness across various scenarios and establishing minimax optimal detection rates.

Contribution

It presents a generic aggregation scheme for change-point detection that adapts to different problems and noise conditions, with proven optimality in several settings.

Findings

Algorithm achieves minimax optimal rates in sparse mean change detection.

Method is adaptable to covariance and nonparametric change-point problems.

Performance is validated under Gaussian and sub-Gaussian noise conditions.

Abstract

This manuscript makes two contributions to the field of change-point detection. In a generalchange-point setting, we provide a generic algorithm for aggregating local homogeneity testsinto an estimator of change-points in a time series. Interestingly, we establish that the errorrates of the collection of tests directly translate into detection properties of the change-pointestimator. This generic scheme is then applied to various problems including covariance change-point detection, nonparametric change-point detection and sparse multivariate mean change-point detection. For the latter, we derive minimax optimal rates that are adaptive to theunknown sparsity and to the distance between change-points when the noise is Gaussian. Forsub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.