Estimating a manifold from noisy samples

Estimating a manifold from (possibly noisy) samples appears to be a difficult problem. Indeed, even after decades of research, all manifold learning methods do not actually “learn” the manifold, but rather try to embed it into a low-dimensional Euclidean space. This process inevitably introduces distortions and cannot guarantee a robust estimate of the manifold.  In this talk, we will discuss a new method to estimate a manifold in the ambient space, which is efficient even in the case of an ambient space of high dimension. The method gives a robust estimate to the manifold and it’s tangent, without introducing distortions. Moreover, we will show statistical convergence guarantees.