Routing for Statistical Inference in Sensor Networks

In the classical approach, the problem of distributed statistical inference and the problem of minimum cost routing of the measurements to the fusion center are treated separately. Such schemes cannot exploit the “inherent” saving in routing costs arising from data reduction in a sufficient statistic for inference. Our approach is to conduct in-network processing of the likelihood function which is the minimal sufficient statistic and deliver it to the fusion center for inference. We employ the Markov random field (MRF) model for spatial correlation of sensor data. The structure of the likelihood function is well known for a MRF from the famous Hammersley-Clifford theorem. Exploiting this structure, we show that the minimum cost routing for computation and delivery of the likelihood function is a Steiner tree on a transformed graph. This Steiner-tree reduction preserves the approximation ratio, which implies that any Steinertree approximation can be employed for minimum cost fusion with the same approximation ratio. In this chapter, we present an overview of this approach to minimum cost fusion.