In this paper, we consider a network scenario in which agents can evaluate each other according to a score graph that models some physical or social interaction. The goal is to design a distributed protocol, run by the agents, allowing them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We prove that each agent can learn its state by combining a local Bayesian classifier with a (centralized) Maximum Likelihood (ML) estimator of the parameter-hyperparameter. To overcome the intractability of the ML problem, we provide two relaxed probabilistic models that lead to distributed estimation schemes with affordable complexity. In order to highlight the appropriateness of the proposed relaxations, we demonstrate the distributed estimators on a machine-to-machine testing setup for anomaly detection and on a social interaction setup for user profiling.