A general framework for deep learning
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Abstract (arXiv)
This paper develops a general approach for deep learning for a setting that includes nonparametric regression and classification. We perform a framework from data that fulfills a generalized Bernstein-type inequality, including independent, φ-mixing, strongly mixing and C-mixing observations. Two estimators are proposed: a non-penalized deep neural network estimator (NPDNN) and a sparse-penalized deep neural network estimator (SPDNN). For each of these estimators, bounds of the expected excess risk on the class of H"older smooth functions and composition H"older functions are established. Applications to independent data, as well as to φ-mixing, strongly mixing, C-mixing processes are considered. For each of these examples, the upper bounds of the expected excess risk of the proposed NPDNN and SPDNN predictors are derived. It is shown that both the NPDNN and SPDNN estimators are minimax optimal (up to a logarithmic factor) in many classical settings.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 16 of its 36 references that are in the map. First posted on arXiv 29 Dec 2025.
Builds on
16 of 36 references.
References · 16
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
- 2018Fast convergence rates of deep neural networks for classificationcited by 46
- 2022Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regressioncited by 31
- 2019Smooth function approximation by deep neural networks with general activation functionscited by 30
- 2022How do noise tails impact on deep ReLU networks?cited by 25
- 2020Quantile regression with deep ReLU Networks: Estimators and minimax ratescited by 24
- 2020Nonconvex sparse regularization for deep neural networks and its optimalitycited by 21
- 2023Classification with Deep Neural Networks and Logistic Losscited by 16
- 2020On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent datacited by 14
- 2022Adaptive deep learning for nonlinear time series modelscited by 11
- 2023Excess risk bound for deep learning under weak dependencecited by 9
- 2023Sparse-penalized deep neural networks estimator under weak dependencecited by 8
4 more
- 2016Learning theory estimates with observations from general stationary stochastic processescited by 7
- 2024Robust deep learning from weakly dependent datacited by 5
- 2024Minimax optimality of deep neural networks on dependent data via PAC-Bayes boundscited by 4
- 2024Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax optimalitycited by 3
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Citing papers per year: 2026: 2.
2 papers.