  Graph-based semi-supervised learning methods combine the graph structure and
labeled data to classify unlabeled data. In this work, we study the effect of a
noisy oracle on classification. In particular, we derive the Maximum A
Posteriori (MAP) estimator for clustering a Degree Corrected Stochastic Block
Model (DC-SBM) when a noisy oracle reveals a fraction of the labels. We then
propose an algorithm derived from a continuous relaxation of the MAP, and we
establish its consistency. Numerical experiments show that our approach
achieves promising performance on synthetic and real data sets, even in the
case of very noisy labeled data.
