18 citations · 37 across the 9 of their papers we have counts for
10 papers
Learning Green's Function Efficiently Using Low-Rank Approximations
Kishan Wimalawarne, Taiji Suzuki, Sophie Langer
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the…
Dropout Regularization Versus -Penalization in the Linear Model
Gabriel Clara, Sophie Langer, Johannes Schmidt-Hieber
We investigate the statistical behavior of gradient descent iterates with dropout in the linear regression model. In particular, non-asymptotic bounds for the convergence of expect…
A novel statistical approach to analyze image classification
Juntong Chen, Sophie Langer, Johannes Schmidt-Hieber
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets d…
Estimation of a regression function on a manifold by fully connected deep neural networks
Michael Kohler, Sophie Langer, Ulrich Reif
Estimation of a regression function from independent and identically distributed data is considered. The error with integration with respect to the distribution of the predic…
Convergence rates for shallow neural networks learned by gradient descent
Alina Braun, Michael Kohler, Sophie Langer +1
In this paper we analyze the error of neural network regression estimates with one hidden layer. Under the assumption that the Fourier transform of the regression function de…
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…