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

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.