Networked Statistical Inference:Cost-Performance Tradeoff

The problem of minimum cost in-network fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center collects all the sensor measurements and performs a statistical-inference test on the measurements, which are spatially correlated according to a Markov random field. Conditioned on the delivery of a sufficient statistic to the fusion center, the fusion scheme minimizing the total routing costs is shown to be a Steiner tree on an expanded graph. This Steiner-tree reduction preserves the approximation ratio, which implies that any Steiner-tree approximation can be employed for minimum cost fusion with the same approximation ratio. The problem is then extended to finding a fusion scheme that achieves optimal tradeoff between the total routing costs and the resulting end inference performance at the fusion center. It is shown that optimal linear tradeoff in a large network has a prize-collecting Steiner tree reduction with the approximation factor preserved. The performance of heuristics for minimum cost fusion are evaluated through theory and simulations, showing a significant saving in routing costs, when compared to routing all the raw measurements to the fusion center.