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.

Start date
Tuesday, Nov. 9, 2021, 1:25 p.m.
End date
Tuesday, Nov. 9, 2021, 2:25 p.m.

Walter Library 402