We just uploaded a new manuscript on consistency of certain semi-supervised learning algorithms on graphs. This joint work with my wonderful collaborators Dr. Franca Hoffmann, Zhi Ren and Prof. Andrew Stuart. The first of multiple papers we’ve been working on where we develop a framework for consistency analysis of semi-supervised learning algorithms.
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data. This paper is concerned with the consistency of optimization-based techniques for such problems, in the limit where the labels have small noise and the underlying unlabelled data is well clustered. We study graph-based probit for binary classification, and a natural generalization of this method to multi-class classification using one-hot encoding. The resulting objective function to be optimized comprises the sum of a quadratic form defined through a rational function of the graph Laplacian, involving only the unlabelled data, and a fidelity term involving only the labelled data. The consistency analysis sheds light on the choice of the rational function defining the optimization.