Quickest Detection of Significant Events in Structured Networks

Abstract

We study the problem of quickest detection of dynamic significant events in structured networks. At some unknown time, an event occurs, and a subset of nodes in the network are affected, which undergo a change in the statistics of their observations. It is assumed that the event propagates dynamically along the edges in the network, in that the affected nodes form a connected subgraph. The event propagation dynamics are 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. We construct a Network-CuSum (N-CuSum) algorithm that exploits network structure in a computationally efficient way. We show that N-CuSum is adaptive to unknown propagation dynamics, and first-order asymptotically optimal as the false alarm rate goes to zero.