Optimality of expectation propagation based distributed estimation for wireless sensor network initialization

We establish that expectation propagation (EP), under some mild requirements and when properly organized, provides sensors with optimal Bayes estimators during the initialization phase of a large randomly deployed wireless sensor network, regardless of the cost function chosen. We are considering the initialization phase to be the period during which the sensors do not yet know their locations and channel/interference strengths, and thus must use random sleep schedules until they have estimated them. During this initialization phase, any other scheme for distributed Bayesian estimation utilizing communication among the same nodes must have equal or worse performance to EP. We discuss the sub-optimality of some other proposed schemes for distributed estimation in sensor networks: consensus propagation and distributed adaptive filtering, arguing that these techniques may presently be seen as seeking suboptimal performance among particular cost functions and with a goal of reduced computation and complexity relative to EP.