Optimizing Graphical Model Structure for Distributed Inference in Wireless Sensor Networks

Graphical models have been widely applied in distributed network computation problems such as inference in large-scale sensor networks. While belief propagation (BP) based on message passing is a powerful approach to solving such distributed inference problems, one major challenge, in the context of wireless sensor networks, is how to systematically address the trade-off between energy efficiency and inference performance. Although various energy-efficient message passing algorithms based on a given graphical model have been proposed in the literature, little work has been done to optimize the graphical model structure to achieve good energy efficiency and inference performance at the same time. In this paper, we propose an efficient distributed algorithm for optimizing the graphical model structure in order to minimize the communication cost required by the inference algorithm without incurring significant performance loss. We first formulate the problem as a multi-objective constrained problem and prove its NP-hardness. Then, we propose an efficient heuristic to solve the problem in polynomial time. Through extensive simulations, using both real-world sensor network data and synthesized data, we empirically evaluate our proposed graphical model structure optimization framework. The simulation results demonstrate that the optimized graphical model efficiently balances the performance of the inference algorithm (measured by mean squared error) and the energy consumed by the inference algorithm (measured by energy used in communication). These highlight the advantages of our proposed framework.