Nearest-neighbor estimation in sensor networks

This contribution reviews some recent advances in the field of nearest-neighbor (NN) nonparametric estimation in sensor networks. Upon observing X₀, the problem is to estimate the corresponding response variable Y₀ by using the knowledge contained in a training set {(X_i, Y_i)}_iⁿ=1, made of n independent copies of (X₀, Y₀). In the distributed version of the problem, a network made of spatially distributed sensors and a common fusion center (FC) is considered. As X₀ is made available at the FC, it is broadcast to all the sensors. Relying upon the locally available pair (X_i, Y_i) and upon X₀, sensor i sends a message containing Y_i to the FC, or stays silent: only the few most informative response variables {Y_i} should be sent, but no inter-sensor coordination is allowed. The analysis is asymptotic in the limit of large network size n and we show that, by means of a suitable ordered transmission policy, only a vanishing fraction of NN messages can be selected, yet preserving the consistency of the estimation even under communication constraints.