9 papers
Convergence rates of deep ReLU networks for multiclass classification
Thijs Bos, Johannes Schmidt-Hieber
For classification problems, trained deep neural networks return probabilities of class memberships. In this work we study convergence of the learned probabilities to the true cond…
The Kolmogorov-Arnold representation theorem revisited
Johannes Schmidt-Hieber
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold repr…
On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints
Kevin Duisters, Johannes Schmidt-Hieber
Frequentist coverage of -highest posterior density (HPD) credible sets is studied in a signal plus noise model under a large class of noise distributions. We consider a spec…
Deep ReLU network approximation of functions on a manifold
Johannes Schmidt-Hieber
Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression probl…
Bayesian variance estimation in the Gaussian sequence model with partial information on the means
Gianluca Finocchio, Johannes Schmidt-Hieber
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bay…
Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery
Markus Reiss, Johannes Schmidt-Hieber
Given data from a Poisson point process with intensity frequentist properties for the Bayesian reconstruction of the support boundary func…