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This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that… Continue Reading
We study first order methods to compute the barycenter of a probability distribution over the Bures-Wasserstein manifold. We derive global rates of convergence for both gradient descent and… Continue Reading
The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model.… Continue Reading
We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and the eigenvalues of the Laplacian and adjacency matrices. Given… Continue Reading