  This paper studies the probability of error associated with the social
machine learning framework, which involves an independent training phase
followed by a cooperative decision-making phase over a graph. This framework
addresses the problem of classifying a stream of unlabeled data in a
distributed manner. In this work, we examine the classification task with
limited observations during the decision-making phase, which requires a
non-asymptotic performance analysis. We establish a condition for consistent
training and derive an upper bound on the probability of error for
classification. The results clarify the dependence on the statistical
properties of the data and the combination policy used over the graph. They
also establish the exponential decay of the probability of error with respect
to the number of unlabeled samples.
