  This work studies the learning process over social networks under partial and
random information sharing. In traditional social learning models, agents
exchange full belief information with each other while trying to infer the true
state of nature. We study the case where agents share information about only
one hypothesis, namely, the trending topic, which can be randomly changing at
every iteration. We show that agents can learn the true hypothesis even if they
do not discuss it, at rates comparable to traditional social learning. We also
show that using one's own belief as a prior for estimating the neighbors'
non-transmitted beliefs might create opinion clusters that prevent learning
with full confidence. This phenomenon occurs when a single hypothesis
corresponding to the truth is exchanged exclusively during all times. Such a
practice, however, avoids the complete rejection of the truth under any
information exchange procedure -- something that could happen if priors were
uniform.

Signal Processing;Multiagent Systems;Social and Information Networks