Non-Parametric Estimation of Manifolds from Noisy Data
In many data-driven applications, the data follows some geometric structure, and the goal is to recover this structure. In many cases, the observed data is noisy and the recovery task is even more challenging. A common assumption is that the data lies on a low dimensional manifold. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there was 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. Moreover, we establish 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 "finding structure in data" using tools from high dimensional analysis, random matrix theory and statistics. The applications for his research include computational biology, manifold learning, and numerical linear algebra.