Talk 1 (15:00): Introduction to Graph-based Learning
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Matthew will give an introduction to graph-based learning, touching on variational problems on graphs, techniques from optimal transport, the calculus of variations, and large data limits.

Talk 2 (16:00): Discrete-To-Continuum Limits in Graph-Based Semi-Supervised Learning

Semi-supervised learning (SSL) is the problem of finding missing labels from a partially labelled data set. The heuristic one uses is that “similar feature vectors should have similar labels”. The notion of similarity between feature vectors explored in this talk comes from a graph-based geometry where an edge is placed between feature vectors that are closer than some connectivity radius. A natural variational solution to the SSL is to minimise a Dirichlet energy built from the graph topology. And a natural question is to ask what happens as the number of feature vectors goes to infinity? In this talk I will give results on the asymptotics of graph-based SSL using an optimal transport topology. The results will include a lower bound on the number of labels needed for consistency.