1 code implementation • 1 Aug 2023 • Kishan Wimalawarne, Taiji Suzuki, Sophie Langer
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations.
no code implementations • 18 Jun 2023 • Gabriel Clara, Sophie Langer, Johannes Schmidt-Hieber
We investigate the statistical behavior of gradient descent iterates with dropout in the linear regression model.
no code implementations • 20 Jul 2021 • Michael Kohler, Sophie Langer, Ulrich Reif
Estimation of a regression function from independent and identically distributed data is considered.
no code implementations • 8 Oct 2020 • Sophie Langer
We ask ourselves if we can show the same approximation rate for a simpler and more general class, i. e., DNNs which are only defined by its width and depth.
no code implementations • 29 Aug 2019 • 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 dimensionality in case that suitable restrictions on the structure of the regression function hold.
no code implementations • 29 Aug 2019 • Michael Kohler, Adam Krzyzak, Sophie Langer
Consequently, the rate of convergence of the estimate does not depend on its input dimension $d$, but on its local dimension $d^*$ and the DNNs are able to circumvent the curse of dimensionality in case that $d^*$ is much smaller than $d$.