Non-Parametric Estimation of Manifolds from Noisy Data

Yariv Aizenbud (Yale University)

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 a 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.

Yariv Aizenbud is a Gibbs assistant professor of applied mathematics at Yale University. Previously, he completed his Ph.D. at Tel-Aviv University. His research is focused on statistical recovery of geometric structures. from data. The applications for his research include computational biology, manifold learning, and numerical linear algebra.