Almost exact recovery in noisy semi-supervised learning

This paper investigates noisy graph-based semi-supervised learning or community detection. We consider the Stochastic Block Model (SBM), where, in addition to the graph observation, an oracle gives a non-perfect information about some nodes' cluster assignment. We derive the Maximum A Priori (MAP) estimator, and show that a continuous relaxation of the MAP performs almost exact recovery under non-restrictive conditions on the average degree and amount of oracle noise. In particular, this method avoids some pitfalls of several graph-based semi-supervised learning methods such as the flatness of the classification functions, appearing in the problems with a very large amount of unlabeled data.