Quickest search for local structures in line networks

A large network of agents in which each agent generates one random variable is considered. The random variables generated by an unknown subset of nodes form a correlation structure, while the remaining nodes generate independent and identically distributed random variables. This paper formalizes and analyzes the quickest search strategy, the goal of which is to identify the unknown subset of correlated nodes with the fewest number of measurements. Despite its widespread applications, the problem of identifying subnetworks with such desired correlation structures is often investigated under the fixed sample-size setting, in which the data acquisition process and the inferential mechanisms are decoupled. Motivated by the significant advantages of sequential detection for agile inference, this paper analyzes this problem under a fully sequential setting. Specifically, it formalizes a framework that incorporates the intertwined processes of data-adaptive information gathering and decision making. Additionally, through a constructive proof, it also offers an optimal sequential data-gathering process as well as the attendant decision rules for identifying a structured subnetwork of interest in a given line network.