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10/04/2022
Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descent
Estimation of a regression function from independent and identically dis...
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08/30/2022
On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descent
Estimation of a multivariate regression function from independent and id...
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05/11/2022
Analysis of convolutional neural network image classifiers in a rotationally symmetric model
Convolutional neural network image classifiers are defined and the rate ...
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11/29/2021
On the rate of convergence of a classifier based on a Transformer encoder
Pattern recognition based on a high-dimensional predictor is considered....
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07/20/2021
The Smoking Gun: Statistical Theory Improves Neural Network Estimates
In this paper we analyze the L_2 error of neural network regression esti...
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07/20/2021
Estimation of a regression function on a manifold by fully connected deep neural networks
Estimation of a regression function from independent and identically dis...
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12/18/2020
On the density estimation problem for uncertainty propagation with unknown input distributions
In this article we study the problem of quantifying the uncertainty in a...
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12/17/2020
Uncertainty Quantification in Case of Imperfect Models: A Review
Uncertainty quantification of complex technical systems is often based o...
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11/27/2020
Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss
Convolutional neural networks learned by minimizing the cross-entropy lo...
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10/31/2020
On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data
A regression problem with dependent data is considered. Regularity assum...
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12/13/2019
Common Voice: A Massively-Multilingual Speech Corpus
The Common Voice corpus is a massively-multilingual collection of transc...
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12/09/2019
Over-parametrized deep neural networks do not generalize well
Recently it was shown in several papers that backpropagation is able to ...
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12/09/2019
Analysis of the rate of convergence of neural network regression estimates which are easy to implement
Recent results in nonparametric regression show that for deep learning, ...
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12/09/2019
On the rate of convergence of a neural network regression estimate learned by gradient descent
Nonparametric regression with random design is considered. Estimates are...
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08/29/2019
Deep Learning and MARS: A Connection
We consider least squares regression estimates using deep neural network...
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08/29/2019