Dynamics and geometry from high dimensional data

Statistical Estimation of Manifolds and Ridges

Larry Wasserman

Carnegie Mellon University

I will first discuss approaches to estimating manifolds based on noisy samples. In general, the best possible rates of convergence are very slow. As an alternative, I'll consider estimating the ridges of the density function. These ridges serve as approximations to the underlying manifold but they can be estimated at a much faster rate. I'll also discuss limiting distribution theory for ridge estimates. This is joint work with Chris Genovese, Marco Perone-Pacifico and Isabella Verdinelli.