The problem of quickest detection of dynamic events in networks is studied. At some unknown time, an event occurs, and a number of nodes in the network are affected by the event, in that they undergo a change in the statistics of their observations. It is assumed that the event is dynamic, in that it can propagate along the edges in the network, and affect more and more nodes with time. The event propagation dynamics is assumed to be unknown. The goal is to design a sequential algorithm that can detect a “significant” event, i.e., when the event has affected no fewer than $\eta $ nodes, as quickly as possible, while controlling the false alarm rate. Fully connected networks are studied first, and the results are then extended to arbitrarily connected networks. The designed algorithms are shown to be adaptive to the unknown propagation dynamics, and their first-order asymptotic optimality is demonstrated as the false alarm rate goes to zero. The algorithms can be implemented with linear computational complexity in the network size at each time step, which is critical for online implementation. Numerical simulations are provided to validate the theoretical results.

中文翻译：

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最快检测网络中的动态事件

研究了网络中动态事件的最快检测问题。在某个未知时间，发生了一个事件，网络中的许多节点都会受到该事件的影响，因为它们的观察统计数据发生了变化。假设事件是动态的，因为它可以沿着网络中的边缘传播，并随着时间影响越来越多的节点。假设事件传播动态未知。目标是设计一种顺序算法，可以检测“重大”事件，即当事件影响不少于 $\eta $ 节点时，尽快，同时控制误报率。首先研究全连接网络，然后将结果扩展到任意连接网络。设计的算法被证明可以适应未知的传播动力学，当误报率变为零时，它们的一阶渐近最优性得到了证明。这些算法可以在每个时间步的网络规模中以线性计算复杂度实现，这对于在线实现至关重要。提供了数值模拟来验证理论结果。