2 citations · 2 across the 6 of their papers we have counts for
8 papers · 1 filter
Higher-order spectral perturbation expansions II: Kernel matrices and manifold learning
Bernhard Stankewitz, Martin Wahl
We study spectral concentration bounds for kernel matrices as approximation of the corresponding kernel integral operator. Results are established under weak assumptions on the dat…
On empirical Hodge Laplacians under the manifold hypothesis
Jan-Paul Lerch, Martin Wahl, Petr Zamolodtchikov
Given i.i.d. observations uniformly distributed on a closed submanifold of the Euclidean space, we study higher-order generalizations of graph Laplacians, so-called Hodge Laplacian…
A kernel-based analysis of Laplacian Eigenmaps
Martin Wahl
Given i.i.d. observations uniformly distributed on a closed manifold , we study the spectral properties of the associated empirical graph Laplaci…
Functional estimation in log-concave location families
Vladimir Koltchinskii, Martin Wahl
Let be a log-concave location family with where is a known convex function and let $X_1,\…
Van Trees inequality, group equivariance, and estimation of principal subspaces
Martin Wahl
We establish non-asymptotic lower bounds for the estimation of principal subspaces. As applications, we obtain new results for the excess risk of principal component analysis and t…
Analyzing the discrepancy principle for kernelized spectral filter learning algorithms
Alain Celisse, Martin Wahl
We investigate the construction of early stopping rules in the nonparametric regression problem where iterative learning algorithms are used and the optimal iteration number is unk…