Learning by gossip: a principled information exchange model in social networks

We cope with the key step of bootstrap methods of generating a possibly infinite sequence of random data preserving properties of the distribution law, starting from a primary sample actually drawn from this distribution. We solve this task in a cooperative way within a community of generators where each improves its performance from the analysis of the other partners' production. Since the analysis is based on an a priori distrust of the other partners' production, we denote the partner ensemble as a gossip community and denote the statistical procedure learning by gossip. We prove that this procedure is highly efficient when applied to the elementary problem of reproducing a Bernoulli distribution, with a properly moderated distrust rate when the absence of a long-term memory requires an online estimation of the bootstrap generator parameters. This fact makes the procedure viable as a basic template of an efficient interaction scheme within social network agents.