In this paper we consider a network scenario in which agents can evaluateeach other according to a score graph that models some physical or socialinteraction. The goal is to design a distributed protocol, run by the agents,allowing them to learn their unknown state among a finite set of possiblevalues. We propose a Bayesian framework in which scores and states areassociated to probabilistic events with unknown parameters and hyperparametersrespectively. We prove that each agent can learn its state by means of a localBayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator ofthe parameter-hyperparameter that combines plain ML and Empirical Bayesapproaches. By using tools from graphical models, which allow us to gaininsight on conditional dependences of scores and states, we provide two relaxedprobabilistic models that ultimately lead to ML parameter-hyperparameterestimators amenable to distributed computation. In order to highlight theappropriateness of the proposed relaxations, we demonstrate the distributedestimators on a machine-to-machine testing set-up for anomaly detection and ona social interaction set-up for user profiling.
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