Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space

DOI10.1214/21-EJS1828zbMath1472.62144arXiv2009.11285MaRDI QIDQ2044364

Kazuma Tsuji, Taiji Suzuki

Publication date: 9 August 2021

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.11285

zbMATH Keywords

neural networknonparametric regressiondeep learningadaptive approximationvariable exponent Besov space

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Learning and adaptive systems in artificial intelligence (68T05) Neural nets and related approaches to inference from stochastic processes (62M45)

Related Items (1)

Drift estimation for a multi-dimensional diffusion process using deep neural networks

Uses Software

• ImageNet
• AlexNet

Cites Work

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• Spatially adaptive density estimation by localised Haar projections
• Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability
• Optimal adaptive sampling recovery
• Spaces of variable smoothness and integrability: characterizations by local means and ball means of differences
• Besov spaces with variable smoothness and integrability
• Minimax risk over hyperrectangles, and implications
• Widths of embeddings in function spaces
• Density estimation in Besov spaces
• Decision theoretic generalizations of the PAC model for neural net and other learning applications
• Wavelets, approximation, and statistical applications
• Information-theoretic determination of minimax rates of convergence
• Wavelet threshold estimation of a regression function with random design
• Kolmogorov widths of the anisotropic Besov classes of periodic functions of many variables
• Locally adaptive confidence bands
• Minimax estimation via wavelet shrinkage
• Density estimation by wavelet thresholding
• Optimal global rates of convergence for nonparametric regression
• Weak convergence and empirical processes. With applications to statistics
• On the minimax optimality and superiority of deep neural network learning over sparse parameter spaces
• Nonparametric regression using deep neural networks with ReLU activation function
• Error bounds for approximations with deep ReLU networks
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• Interpolation of Besov Spaces
• A Lower Bound on the Risks of Non-Parametric Estimates of Densities in the Uniform Metric
• Besov Spaces on Domains in ℝ d

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