Coarse Ricci curvature and the manifold learning problem

Coarse Ricci curvature and the manifold learning problem

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Antonio Ache , Princeton University
Fine Hall 314

We use the framework exploited by Bakry and Emery for the study of logarithmic Sobolev inequalities to consider the statistical problem of estimating the Ricci curvature (and more generally the Bakry-Emery tensor of a manifold with density) of an embedded submanifold of Euclidean space from a point cloud drawn from the submanifold. Our method leads to a definition of Coarse Ricci curvature alternative to the one proposed by Y. Ollivier. This is joint work with Micah Warren.