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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...
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06/18/2023
A supervised deep learning method for nonparametric density estimation
Nonparametric density estimation is an unsupervised learning problem. In...
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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...
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03/14/2023
Codivergences and information matrices
We propose a new concept of codivergence, which quantifies the similarit...
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01/27/2023
Interpreting learning in biological neural networks as zero-order optimization method
Recently, significant progress has been made regarding the statistical u...
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06/05/2022
A statistical analysis of an image classification problem
The availability of massive image databases resulted in the development ...
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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...
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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 ...
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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...
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08/02/2021
Convergence rates of deep ReLU networks for multiclass classification
For classification problems, trained deep neural networks return probabi...
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05/16/2021
Posterior contraction for deep Gaussian process priors
We study posterior contraction rates for a class of deep Gaussian proces...
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07/31/2020
The Kolmogorov-Arnold representation theorem revisited
There is a longstanding debate whether the Kolmogorov-Arnold representat...
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05/30/2020
On lower bounds for the bias-variance trade-off
It is a common phenomenon that for high-dimensional and nonparametric st...
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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...
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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...
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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...
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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)≤ ...
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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...
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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...
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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...
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08/22/2017