Non-Parametric Estimation of Manifolds from Noisy Data

Applied and Computational Mathematics Seminar
Monday, December 6, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Yariv Aizenbud – Yale University – yariv.aizenbud@yale.edu
Wenjing Liao
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.