This thesis uses Kantorovich-Rubinstein distance for classifying points based on their measures.
arXiv research
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Revisits shallow neural networks using Lipschitz norms and measures.
Study sharp convergence rates of empirical UOT for spatio-temporal point processes.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
New framework enhances neural network robustness against adversarial attacks.
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they…
Paper tackles distribution matching by partially matching distributions, achieving robust results.
New neural method calculates EMD for particle physics data.
Paper relaxes the Lipschitz constraint in WGANs to improve performance.
Efficiently simulates and calibrates the rough Bergomi model using Wasserstein distance.