Optimal nonparametric inference via deep neural network

DOI10.1016/j.jmaa.2021.125561zbMath1476.62066arXiv1902.01687OpenAlexW3190727821MaRDI QIDQ2235970

Ben Boukai, Zuofeng Shang, Rui-Qi Liu

Publication date: 22 October 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01687

zbMATH Keywords

asymptotic distributionnonparametric inferencenonparametric testingtensor product B-splinesdeep neural networkoptimal minimax risk bound

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Numerical computation using splines (65D07) Nonparametric estimation (62G05) Artificial neural networks and deep learning (68T07) Neural nets and related approaches to inference from stochastic processes (62M45)

Related Items

Deep neural network classifier for multidimensional functional data, Nonparametric regression with modified ReLU networks, Robust deep neural network estimation for multi-dimensional functional data

Cites Work

• Unnamed Item
• Analysis of the rate of convergence of least squares neural network regression estimates in case of measurement errors
• Additive regression and other nonparametric models
• A practical guide to splines
• The use of polynomial splines and their tensor products in multivariate function estimation. (With discussion)
• Asymptotically minimax hypothesis testing for nonparametric alternatives. I
• Local asymptotics for polynomial spline regression
• Projection estimation in multiple regression with application to functional ANOVA models
• Nonparametric regression using deep neural networks with ReLU activation function
• Error bounds for approximations with deep ReLU networks
• Nonasymptotic bounds on the \(L_{2}\) error of neural network regression estimates
• Adaptive regression estimation with multilayer feedforward neural networks
• Deep Neural Networks for Estimation and Inference
• Nonparametric Regression Based on Hierarchical Interaction Models