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Many analytical and geometrical notions at the continuum level can be analyzed by interpreting them in Wasserstein spaces, hence it is natural to do the same at the sample level. The relevant question is when are these notions stable as the sample size grows to infinity? The main result can be used to establish a variety of consistency results for evolutions of gradient flow type that are relevant to tasks like manifold learning and clustering.
This presentation is part of Minisymposium “MS17 - Discrete-to-continuum graphical methods for large-data clustering, classification and segmentation”
organized by: Matthew Thorpe (University of Cambridge) , Luca Calatroni (CMAP, École Polytechnique CNRS) , Daniel Tenbrinck (University of Münster) .