Title: Interaction-Based Distributed Learning in Cyber-Physical and Social Networks,
Abstract: 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 means of a local
Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of
the parameter-hyperparameter that combines plain ML and Empirical Bayes
approaches. By using tools from graphical models, which allow us to gain
insight on conditional dependences of scores and states, we provide two relaxed
probabilistic models that ultimately lead to ML parameter-hyperparameter
estimators amenable to distributed computation. In order to highlight the
appropriateness of the proposed relaxations, we demonstrate the distributed
estimators on a machine-to-machine testing set-up for anomaly detection and on
a social interaction set-up for user profiling.