IMA Data Science Seminar: Non-Parametric Estimation of Manifolds from Noisy Data

The Institute for Mathematics and Its Applications (IMA) Data Science Seminars are a forum for data scientists of IMA academic and industrial partners to discuss and learn about recent developments in the broad area of data science. The seminars take place on Tuesdays from 1:25 p.m. - 2:25 p.m.

This week's speaker, Yariv Aizenbud (Yale University), will be giving a talk titled "Non-Parametric Estimation of Manifolds from Noisy Data."

You may attend the talk either in person in Walter 402 or registering via Zoom.

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 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.

Biography

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.