A Coalitional Game for Distributed Inference in Sensor Networks with Dependent Observations

We consider the problem of collaborative inference in a sensor network with heterogeneous and statistically dependent sensor observations. Each sensor aims to maximize its inference performance by forming a coalition with other sensors and sharing information within the coalition. In this paper, the formation of non-overlapping coalitions with statistically dependent sensors is investigated under a communication constraint. We apply a game theoretical approach to fully explore and utilize the information contained in the spatial dependence among sensors to maximize individual sensor performance. Before formulating the distributed inference problem as a coalition formation game, we quantify the gain and loss in forming a coalition by introducing the concepts of diversity gain and redundancy loss for both estimation and detection problems. These definitions, enabled by the statistical theory of copulas, allow us to characterize the influence of statistical dependence among sensor observations on inference performance and collaboration strategy. An iterative algorithm based on merge-and-split operations is proposed for the solution and the stability of the proposed algorithm is analyzed. Numerical results are also provided for illustration.