Coarse Ricci curvature and the manifold learning problem

Friday, September 12, 2014 -
3:00pm to 4:00pm
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. 
Speaker: 
Antonio Ache
Princeton University
Event Location: 
Fine Hall 314