Generalized multiple change-point detection in the structure of multivariate, possibly high-dimensional, data sequences

TL;DR

This paper introduces the Multivariate Isolate-Detect (MID) algorithm for consistent detection of multiple change-points in high-dimensional multivariate data sequences, capable of handling frequent, small-magnitude changes efficiently.

Contribution

It presents a novel, computationally fast method for detecting multiple change-points in high-dimensional data, accommodating structural changes in mean vectors and linear trends.

Findings

MID achieves consistent change-point detection in high-dimensional settings.

The method handles frequent, small-magnitude changes effectively.

It scales well with increasing data size and dimensionality.

Abstract

The extensive emergence of big data techniques has led to an increasing interest in the development of change-point detection algorithms that can perform well in a multivariate, possibly high-dimensional setting. In the current paper, we propose a new method for the consistent estimation of the number and location of multiple generalized change-points in multivariate, possibly high-dimensional, noisy data sequences. The number of change-points is allowed to increase with the sample size and the dimensionality of the given data sequence. Having a number of univariate signals, which constitute the unknown multivariate signal, our algorithm can deal with general structural changes; we focus on changes in the mean vector of a multivariate piecewise-constant signal, as well as changes in the linear trend of any of the univariate component signals. Our proposed algorithm, labeled Multivariate Isolate-Detect (MID), allows for consistent change-point detection in the presence of frequent changes of possibly small magnitudes in a computationally fast way.