Search Results for author: Sophie Langer

Found 6 papers, 1 papers with code

Learning Green's Function Efficiently Using Low-Rank Approximations

1 code implementation1 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.

Dropout Regularization Versus $\ell_2$-Penalization in the Linear Model

no code implementations18 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.

regression

Estimation of a regression function on a manifold by fully connected deep neural networks

no code implementations20 Jul 2021 Michael Kohler, Sophie Langer, Ulrich Reif

Estimation of a regression function from independent and identically distributed data is considered.

regression

Approximating smooth functions by deep neural networks with sigmoid activation function

no code implementations8 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.

On the rate of convergence of fully connected very deep neural network regression estimates

no code implementations29 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.

regression

Estimation of a function of low local dimensionality by deep neural networks

no code implementations29 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 $d$.

Dimensionality Reduction object-detection +4

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