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

TL;DR

This paper introduces a game-theoretic framework for forming sensor coalitions in distributed inference tasks, leveraging statistical dependence to optimize performance while considering energy constraints.

Contribution

It develops a novel coalition formation game using copula-based dependence measures, balancing inference gains and energy costs in sensor networks.

Findings

Coalition size increases inference performance but also energy consumption.

The proposed merge-and-split algorithm achieves stable coalition structures.

Numerical results show the approach outperforms existing methods.

Abstract

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. It is proved that the inference performance is a nondecreasing function of the coalition size. However, in an energy constrained network, the energy consumption of inter-sensor communication also increases with increasing coalition size, which discourages the formation of the grand coalition (the set of all sensors). In this paper, the formation of non-overlapping coalitions with statistically dependent sensors is investigated under a specific 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 first 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. 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 provided to demonstrate the superiority of our proposed game theoretical approach.