8 citations · 22 across the 19 of their papers we have counts for
23 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…
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…
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…
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…
A note on the prediction error of principal component regression in high dimensions
Laura Hucker, Martin Wahl
We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first ma…
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 in…
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…
Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses
Niklas Hartung, Martin Wahl, Abhishake Rastogi +1
The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. While covariate selection criteria have been studie…
Lower bounds for invariant statistical models with applications to principal component analysis
Martin Wahl
This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the sp…
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…
On the perturbation series for eigenvalues and eigenprojections
Martin Wahl
A standard perturbation result states that perturbed eigenvalues and eigenprojections admit a perturbation series provided that the operator norm of the perturbation is smaller tha…
High-probability bounds for the reconstruction error of PCA
Cassandra Milbradt, Martin Wahl
We derive high-probability bounds for the reconstruction error of PCA in infinite dimensions. We apply our bounds in the case that the eigenvalues of the covariance operator satisf…
A note on the prediction error of principal component regression
Martin Wahl
We analyse the prediction error of principal component regression (PCR) and prove non-asymptotic upper bounds for the corresponding squared risk. Under mild assumptions, we show th…
Perturbation bounds for eigenspaces under a relative gap condition
Moritz Jirak, Martin Wahl
A basic problem in operator theory is to estimate how a small perturbation effects the eigenspaces of a self-adjoint compact operator. In this paper, we prove upper bounds for the…
Relative perturbation bounds with applications to empirical covariance operators
Moritz Jirak, Martin Wahl
The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spec…
Functional estimation and hypothesis testing in nonparametric boundary models
Markus Reiß, Martin Wahl
Consider a Poisson point process with unknown support boundary curve , which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear…
Non-asymptotic upper bounds for the reconstruction error of PCA
Markus Reiß, Martin Wahl
We analyse the reconstruction error of principal component analysis (PCA) and prove non-asymptotic upper bounds for the corresponding excess risk. These bounds unify and improve ex…
Statistical inference in sparse high-dimensional additive models
Karl Gregory, Enno Mammen, Martin Wahl
In this paper we discuss the estimation of a nonparametric component of a nonparametric additive model . We allow the number of additive c…
Variable selection in high-dimensional additive models based on norms of projections
Martin Wahl
We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The…
A theory of nonparametric regression in the presence of complex nuisance components
Martin Wahl
In this paper, we consider the nonparametric random regression model and address the problem of estimating the function . The term is regard…
On the mod-Gaussian convergence of a sum over primes
Martin Wahl
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates . This Dirichlet polynomial is sufficiently long to deduce Selberg's…