4 papers
Analysis of the rate of convergence of fully connected deep neural network regression estimates with smooth activation function
Sophie Langer
This article contributes to the current statistical theory of deep neural networks (DNNs). It was shown that DNNs are able to circumvent the so--called curse of dimensionality in c…
Approximating smooth functions by deep neural networks with sigmoid activation function
Sophie Langer
We study the power of deep neural networks (DNNs) with sigmoid activation function. Recently, it was shown that DNNs approximate any -dimensional, smooth function on a compact s…
Estimation of a function of low local dimensionality by deep neural networks
Michael Kohler, Adam Krzyzak, Sophie Langer
Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is n…
On the rate of convergence of fully connected very deep neural network regression estimates
Michael Kohler, Sophie Langer
Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensiona…