Distributed learning from social sampling

We describe a general set of protocols for distributed estimation of distributions in a network. This work falls in the framework of consensus or gossip algorithms - individuals have local observations of a global phenomenon and wish to estimate a global quantity through synchronous (consensus) or asynchronous (gossip) protocols. Our approach departs from consensus-based models of communication by using a message model based on the exchange of randomly selected messages. In most cases these messages are much simpler to transmit than the full state information required by a consensus protocols. In other words, agents collect information and form beliefs via sampling: agents take local (noisy) samples of the global phenomenon of interest and social samples from the belief neighbors in the network. We propose an appropriate analytic framework and provide examples to demonstrate how social sampling can enable social learning.