Optimal combination rules for adaptation and learning over networks

Adaptive networks, consisting of a collection of nodes with learning abilities, are well-suited to solve distributed inference problems and to model various types of self-organized behavior observed in nature. One important issue in designing adaptive networks is how to fuse the information collected from the neighbors, especially since the mean-square performance of the network depends on the choice of combination weights. We consider the problem of optimal selection of the combination weights and motivate one combination rule, along with an adaptive implementation. The rule is related to the inverse of the noise variances and is shown to be effective in simulations.