5 papers
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…
Concentration and moment inequalities for sums of independent heavy-tailed random matrices
Moritz Jirak, Stanislav Minsker, Yiqiu Shen +1
We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only…
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…
Optimal parameter estimation for linear SPDEs from multiple measurements
Randolf Altmeyer, Anton Tiepner, Martin Wahl
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the…
Quantitative limit theorems and bootstrap approximations for empirical spectral projectors
Moritz Jirak, Martin Wahl
Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator , the problem of recovering the spectral projectors of naturally arises i…