Nonasymptotic rates for manifold, tangent space and curvature estimation
Nonasymptotic rates for manifold, tangent space and curvature estimation
Given a noisy sample from a submanifold $M\subset\mathbb{R}^{D}$, we derive optimal rates for the estimation of tangent spaces $T_{X}M$, the second fundamental form $\mathit{II}_{X}^{M}$ and the submanifold $M$. After motivating their study, we introduce a quantitative class of $\mathcal{C}^{k}$-submanifolds in analogy with Hölder classes. The proposed estimators are based on …