论文标题
在线分数统计信息，用于检测网络点过程中的聚类变化
Online Score Statistics for Detecting Clustered Change in Network Point Processes
论文作者
论文摘要
我们考虑对网络事件数据的在线监视，以检测受影响的数据流分布从一个点进程转移到其他参数的另一个过程时的群集中的本地变化。具体而言，我们有兴趣检测一个变化点，该变化点会导致基础数据分布的转移，该数据分布遵循多元鹰队的过程，并具有指数衰减的时间内核，因此，霍克斯过程被认为是对观测之间的时空相关性的说明。拟议的检测程序基于扫描评分统计。我们得出了统计量的渐近分布，从而实现了自称属性，并促进了瞬时错误警报概率和平均运行长度的近似。当检测霍克斯过程的变化中，没有散布自我激发时，该过程不需要估计变换后网络参数，同时假定具有计算效率的时间衰减参数。我们进一步提出了一个有效的程序，可以通过重要性采样来准确确定错误的发现率，如数值示例验证。使用模拟和真实的证券交易所数据，我们显示了所提出的方法在享受计算效率的同时检测变化的有效性。
We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution that follows a multivariate Hawkes process with exponential decay temporal kernel, whereby the Hawkes process is considered to account for spatio-temporal correlation between observations. The proposed detection procedure is based on scan score statistics. We derive the asymptotic distribution of the statistic, which enables the self-normalizing property and facilitates the approximation of the instantaneous false alarm probability and the average run length. When detecting a change in the Hawkes process with non-vanishing self-excitation, the procedure does not require estimating the post-change network parameter while assuming the temporal decay parameter, which enjoys computational efficiency. We further present an efficient procedure to accurately determine the false discovery rate via importance sampling, as validated by numerical examples. Using simulated and real stock exchange data, we show the effectiveness of the proposed method in detecting change while enjoying computational efficiency.
