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.

翻译：变化点分析已被成功应用于检测多变量数据流随时间的变化。在许多应用中，当数据基于图/网络进行观测时，变化并非同时发生，而是随时间从初始源坐标向邻近坐标传播。我们提出了一种新方法SpreadDetect，用于估计此类情境下的变化源坐标和初始时间点。我们证明，在适当条件下，SpreadDetect算法能够一致地估计源坐标和变化时间点，且该算法可检测的最小信号规模达到极小化最优。通过数值实验和COVID-19真实数据集验证了该算法的实际效用。