Johannes Schmidt-Hieber | DeepAI

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∙ 06/18/2023

Dropout Regularization Versus ℓ_2-Penalization in the Linear Model

We investigate the statistical behavior of gradient descent iterates wit...

0 Gabriel Clara, et al. ∙

∙ 06/18/2023

A supervised deep learning method for nonparametric density estimation

Nonparametric density estimation is an unsupervised learning problem. In...

0 Thijs Bos, et al. ∙

∙ 03/21/2023

Lower bounds for the trade-off between bias and mean absolute deviation

It is a widely observed phenomenon in nonparametric statistics that rate...

0 Alexis Derumigny, et al. ∙

∙ 03/14/2023

Codivergences and information matrices

We propose a new concept of codivergence, which quantifies the similarit...

0 Alexis Derumigny, et al. ∙

∙ 01/27/2023

Interpreting learning in biological neural networks as zero-order optimization method

Recently, significant progress has been made regarding the statistical u...

0 Johannes Schmidt-Hieber, et al. ∙

∙ 06/05/2022

A statistical analysis of an image classification problem

The availability of massive image databases resulted in the development ...

0 Sophie Langer, et al. ∙

∙ 05/16/2022

On the inability of Gaussian process regression to optimally learn compositional functions

We rigorously prove that deep Gaussian process priors can outperform Gau...

0 Matteo Giordano, et al. ∙

∙ 04/11/2022

Local convergence rates of the least squares estimator with applications to transfer learning

Convergence properties of empirical risk minimizers can be conveniently ...

0 Johannes Schmidt-Hieber, et al. ∙

∙ 01/12/2022

On generalization bounds for deep networks based on loss surface implicit regularization

The classical statistical learning theory says that fitting too many par...

31 Masaaki Imaizumi, et al. ∙

∙ 08/02/2021

Convergence rates of deep ReLU networks for multiclass classification

For classification problems, trained deep neural networks return probabi...

0 Thijs Bos, et al. ∙

∙ 05/16/2021

Posterior contraction for deep Gaussian process priors

We study posterior contraction rates for a class of deep Gaussian proces...

0 Gianluca Finocchio, et al. ∙

∙ 07/31/2020

The Kolmogorov-Arnold representation theorem revisited

There is a longstanding debate whether the Kolmogorov-Arnold representat...

0 Johannes Schmidt-Hieber, et al. ∙

∙ 05/30/2020

On lower bounds for the bias-variance trade-off

It is a common phenomenon that for high-dimensional and nonparametric st...

0 Alexis Derumigny, et al. ∙

∙ 03/09/2020

On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints

Frequentist coverage of (1-α)-highest posterior density (HPD) credible s...

0 Kevin Duisters, et al. ∙

∙ 08/02/2019

Deep ReLU network approximation of functions on a manifold

Whereas recovery of the manifold from data is a well-studied topic, appr...

0 Johannes Schmidt-Hieber, et al. ∙

∙ 04/09/2019

Bayesian variance estimation in the Gaussian sequence model with partial information on the means

Consider the Gaussian sequence model under the additional assumption tha...

0 Gianluca Finocchio, et al. ∙

∙ 09/11/2018

Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery

Given data from a Poisson point process with intensity (x,y) n 1(f(x)≤ ...

0 Markus Reiß, et al. ∙

∙ 09/07/2018

Posterior consistency for n in the binomial (n,p) problem with both parameters unknown - with applications to quantitative nanoscopy

The estimation of the population size n from k i.i.d. binomial observati...

0 Laura Fee Schneider, et al. ∙

∙ 04/06/2018

A comparison of deep networks with ReLU activation function and linear spline-type methods

Deep neural networks (DNNs) generate much richer function spaces than sh...

0 Konstantin Eckle, et al. ∙

∙ 02/09/2018

Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities

It is well-known that density estimation on the unit interval is asympto...

0 Kolyan Ray, et al. ∙

∙ 08/22/2017

Nonparametric regression using deep neural networks with ReLU activation function

Consider the multivariate nonparametric regression model. It is shown th...

0 Johannes Schmidt-Hieber, et al. ∙

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