2 citations · 2 across the 4 of their papers we have counts for
7 papers
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…
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…