Abstract
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.
Highlights
I N THE problem of quickest change detection (QCD), a stochastic system is observed sequentially
We show that the generalized log-likelihood ratio test is equivalent to one that compares the sum of the smallest L − η + 1 local Cumulative Sum (CuSum) statistics [37] to the same threshold
We further show that the S-CuSum algorithm satisfies the false alarm constraints with a properly chosen threshold for all scenarios with fewer than η affected nodes, and adapts to unknown event propagation dynamics
Summary
I N THE problem of quickest change detection (QCD), a stochastic system is observed sequentially. A change occurs that changes the data generating process. Observations are taken sequentially with time, and the objective is to detect the change as quickly as Manuscript received July 17, 2018; revised October 10, 2019; accepted October 13, 2019. This article was presented in part at the 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, and in part at the Asilomar Conference on Signals, Systems, and Computers
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