Mathematics Information and Applications Seminar: Dr Bamdad Hosseini

Graphical semi-supervised learning is the problem of labelling the verticess of a graph given the labels of a a few vertices along with geometric information about the graph. Such problems have attracted a lot of attention in machine learning for classification of large datasets. In this talk we discuss consistency and perturbation properties of the probit approach to semi-supervised learning-- an approach that relaxes semi-supervised learning to a convex optimization problem. We show that the probit solution is unique and the predicted labels are consistent with the true labels of the vertices under some conditions. Furthermore, we study the probit approach in the large data limit where the number of vertices tends to infinity. In this limit, the probit approach converges to a convex optimization problem for functions. We then present analogous consistency and perturbation results for this limiting optimization problem.