66 citations · 124 across the 22 of their papers we have counts for
6 papers · 1 filter
On the density estimation problem for uncertainty propagation with unknown input distributions
Sebastian Kersting, Michael Kohler
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the te…
Uncertainty Quantification in Case of Imperfect Models: A Review
Sebastian Kersting, Michael Kohler
Uncertainty quantification of complex technical systems is often based on a computer model of the system. As all models such a computer model is always wrong in the sense that it d…
Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss under the hierarchical max-pooling model
Michael Kohler, Sophie Langer
Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also…
On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data
Michael Kohler, Adam Krzyzak
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumpti…
On the rate of convergence of image classifiers based on convolutional neural networks
M. Kohler, A. Krzyzak, B. Walter
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassificati…
Over-parametrized deep neural networks do not generalize well
Michael Kohler, Adam Krzyzak
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural netwo…