2 research outputs found
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
Almost Exact Recovery in Label Spreading
International audienceIn semi-supervised graph clustering setting, an expert provides cluster membership of few nodes. This little amount of information allows one to achieve high accuracy clustering using efficient computational procedures. Our main goal is to provide a theoretical justification why the graph-based semi-supervised learning works very well. Specifically, for the Stochastic Block Model in the moderately sparse regime, we prove that popular semi-supervised clustering methods like Label Spreading achieve asymptotically almost exact recovery as long as the fraction of labeled nodes does not go to zero and the average degree goes to infinity