Non-Bayesian Social Learning With Gaussian Uncertain Models

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through likelihood updates from their observations. Typically, likelihood models are assumed known precisely. However, in many situations the models are generated from sparse training data due to lack of data availability, high cost of collection/calibration, limits within the communications network, and/or the high dynamics of the operational environment. Recently, social learning theory was extended to handle those model uncertainties for categorical models. In this paper, we introduce the theory of Gaussian uncertain models and study the properties of the beliefs generated by the network of agents. We show that even with finite amounts of training data, non-Bayesian social learning can be achieved and all agents in the network will converge to a consensus belief that provably identifies the best estimate for the state of the world given the set of prior information.