SpreadDetect: Detection of spreading change in a network over time

Abstract

Change-point analysis has been successfully applied to the detect changes in multivariate data streams over time. In many applications, when data are observed over a graph/network, change does not occur simultaneously but instead spread from an initial source coordinate to the neighbouring coordinates over time. We propose a new method, SpreadDetect, that estimates both the source coordinate and the initial timepoint of change in such a setting. We prove that under appropriate conditions, the SpreadDetect algorithm consistently estimates both the source coordinate and the timepoint of change and that the minimal signal size detectable by the algorithm is minimax optimal. The practical utility of the algorithm is demonstrated through numerical experiments and a COVID-19 real dataset.