[Paper Review] Quickest Detection of Dynamic Events in Networks

Shaofeng Zou, Venugopal V. Veeravalli+2 more|arXiv (Cornell University)|Jul 16, 2018

Distributed Sensor Networks and Detection Algorithms31 references4 citations

TL;DR

This paper proposes a sequential detection algorithm for identifying dynamic events in networks that propagate over time and affect an increasing number of nodes. The method uses a modified CUSUM statistic across connected node subsets to detect when at least η nodes are affected, achieving first-order asymptotic optimality with linear computational complexity and controlled false alarm rates as the threshold increases.

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 $η$ 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.

Motivation & Objective

• To detect dynamic events in networks that propagate over time and affect an increasing number of nodes.
• To design a sequential algorithm that identifies when a 'significant' event—defined as affecting at least η nodes—occurs as quickly as possible.
• To ensure the algorithm is adaptive to unknown propagation dynamics and maintains a controlled false alarm rate.
• To achieve linear computational complexity per time step for real-time online deployment.
• To extend the framework from fully connected to arbitrarily connected networks with structured propagation.

Proposed method

• The algorithm uses a modified CUSUM statistic on subsets of nodes to detect changes in observation statistics across the network.
• It employs a sliding window of log-likelihood ratios to track changes in node behavior over time.
• The detection threshold is based on a cumulative sum over all η-node connected subsets, minimizing the detection delay.
• The method uses a recursive structure to maintain computational efficiency and enable online implementation.
• It leverages the network topology to restrict detection to connected subgraphs, ensuring physical plausibility of propagation.
• Theoretical analysis uses the Weak Law of Large Numbers and bounds on tail probabilities to establish asymptotic optimality.

Experimental results

Research questions

• RQ1 How can a sequential detection algorithm be designed to detect dynamic events in networks that propagate over time with unknown dynamics?
• RQ2 What is the optimal trade-off between detection delay and false alarm rate when the event affects a minimum of η nodes?
• RQ3 Can the algorithm maintain first-order asymptotic optimality without prior knowledge of the event propagation order or timing?
• RQ4 How can the algorithm be implemented with linear computational complexity in network size for real-time deployment?
• RQ5 What is the performance gain of using network topology-aware detection compared to non-topology-aware methods?

Key findings

• The proposed algorithm achieves first-order asymptotic optimality as the false alarm rate approaches zero, meaning it minimizes detection delay relative to the theoretical lower bound.
• The expected detection delay is bounded by O(b) as the threshold b increases, with the constant factor approaching the theoretical minimum.
• The algorithm maintains linear computational complexity O(L) per time step, where L is the number of nodes, enabling real-time implementation.
• The false alarm probability decays exponentially with the threshold b, ensuring strong control over false positives.
• The method is robust to unknown propagation dynamics and performs well even when the event spreads along arbitrary network topologies.
• Numerical simulations validate the theoretical results, showing fast detection and low false alarm rates in both fully connected and sparse networks.