Quickest Detection of Markov Networks
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Detecting correlation structures in large networks arises in many domains. Such detection problems are often studied independently of the underlying data acquisition process, rendering settings in which data acquisition policies (e.g., the sample-size) are pre-specified. Motivated by the advantages of data-adaptive sampling, this paper treats the inherently coupled problems of data acquisition and decision-making for correlation detection. Specifically, this paper considers a Markov network of agents generating random variables, and designs a quickest sequential strategy for discerning the correlation model governing the Markov network. By abstracting the Markov network as an undirected graph,designing the quickest sampling strategy becomes equivalent to sequentially and data-adaptively identifying and sampling a sequence of vertices in the graph. The existing data-adaptive approaches fail to solve this problem since the node selection actions are dependent. Hence, a novel sampling strategy is proposed to incorporate the correlation structures into the decision rules for minimizing the average delay in forming a confident decision. The proposed procedure involves searching over all possible future decisions which becomes computationally prohibitive for large networks. However, by leveraging the Markov properties it is shown that the search horizon can be reduced to the neighbors of each node in the dependency graph without compromising the performance. Performance analyses and numerical evaluations demonstrate the gains of the proposed sequential approach over the existing ones.
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