Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors
Author:
Affiliation:
1. School of Mathematics and Statistics, Wuhan University
2. Department of Applied Mathematics, Hong Kong Polytechnic University
3. Department of Statistics, Chinese University of Hong Kong
Publisher
Institute of Mathematical Statistics
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Reference92 articles.
1. Bickel, P. J. and Li, B. (2007). Local polynomial regression on unknown manifolds. In Complex Datasets and Inverse Problems. Institute of Mathematical Statistics Lecture Notes—Monograph Series 54 177–186. IMS, Beachwood, OH.
2. Falconer, K. (2003). Fractal Geometry: Mathematical Foundations and Applications, 2nd ed. Wiley, Hoboken, NJ.
3. Yang, Y. and Dunson, D. B. (2016). Bayesian manifold regression. Ann. Statist. 44 876–905.
4. Stone, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 590–606.
5. Birgé, L. and Massart, P. (1998). Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 329–375.
Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Robust nonparametric regression based on deep ReLU neural networks;Journal of Statistical Planning and Inference;2024-12
2. Deep learning based on randomized quasi-Monte Carlo method for solving linear Kolmogorov partial differential equation;Journal of Computational and Applied Mathematics;2024-12
3. Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis;East Asian Journal on Applied Mathematics;2024-06
4. Low dimensional approximation and generalization of multivariate functions on smooth manifolds using deep ReLU neural networks;Neural Networks;2024-06
5. Neural networks meet random forests;Journal of the Royal Statistical Society Series B: Statistical Methodology;2024-05-22
1.学者识别学者识别
2.学术分析学术分析
3.人才评估人才评估
"同舟云学术"是以全球学者为主线，采集、加工和组织学术论文而形成的新型学术文献查询和分析系统，可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容，当前同舟云学术共收录了国内外主流学术期刊6万余种，收集的期刊论文及会议论文总量共计约1.5亿篇，并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询！咨询电话：010-8811{复制后删除}0370
www.globalauthorid.com
TOP
Copyright © 2019-2024 北京同舟云网络信息技术有限公司 京公网安备11010802033243号 京ICP备18003416号-3