Title: Non-Parametric Estimation of Manifolds from Noisy Data

Abstract: A common task in many data-driven applications is to find a low dimensional manifold that describes the data accurately. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there is no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples with constant level of noise. 

In this talk, we will present a method that estimates a manifold and its tangent in the ambient space. Moreover, we establish rigorous convergence rates, which are essentially as good as existing convergence rates for function estimation.

This is a joint work with Barak Sober.