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08/01/2023
Learning Green's Function Efficiently Using Low-Rank Approximations
Learning the Green's function using deep learning models enables to solv...
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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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06/05/2022
A statistical analysis of an image classification problem
The availability of massive image databases resulted in the development ...
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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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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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10/12/2020
Analysis of the rate of convergence of fully connected deep neural network regression estimates with smooth activation function
This article contributes to the current statistical theory of deep neura...
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10/08/2020
Approximating smooth functions by deep neural networks with sigmoid activation function
We study the power of deep neural networks (DNNs) with sigmoid activatio...
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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