mlsanityData to 7 Oct 2026

Excess risk bound for deep learning under weak dependence

arXiv 2302.07503 ↗First posted 15 Feb 2023stat.ML cs.LGcited by 9

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Abstract (arXiv)

This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The psi-weak dependence structure considered is quite large and covers other conditions such as mixing, association,ldots Firstly, the approximation of smooth functions by deep neural networks with a broad class of activation functions is considered. We derive the required depth, width and sparsity of a deep neural network to approximate any H"older smooth function, defined on any compact set mx. Secondly, we establish a bound of the excess risk for the learning of weakly dependent observations by deep neural networks. When the target function is sufficiently smooth, this bound is close to the usual O(n-1/2).

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 12 of its 27 references that are in the map. First posted on arXiv 15 Feb 2023.

Builds on

12 of 27 references.

References · 12

  1. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  2. 2016Error bounds for approximations with deep ReLU networkscited by 567
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  5. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
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  7. 2018Fast convergence rates of deep neural networks for classificationcited by 46
  8. 2019Smooth function approximation by deep neural networks with general activation functionscited by 29
  9. 2020Nonconvex sparse regularization for deep neural networks and its optimalitycited by 21
  10. 2022Theoretical analysis of deep neural networks for temporally dependent observationscited by 16
  11. 2020On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent datacited by 14
  12. 2017Improving Deep Learning by Inverse Square Root Linear Units (ISRLUs)cited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 1; 2026: 2.

9 papers.

  1. 2023Sparse-penalized deep neural networks estimator under weak dependencecited by 8
  2. 2024Robust deep learning from weakly dependent datacited by 5
  3. 2024Minimax optimality of deep neural networks on dependent data via PAC-Bayes boundscited by 4
  4. 2024Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax optimalitycited by 3
  5. 2023Penalized deep neural networks estimator with general loss functions under weak dependencecited by 2
  6. 2024Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approachcited by 2
  7. 2025A general framework for deep learningcited by 2
  8. 2026Deep regression learning from dependent observations with minimum error entropy principlecited by 0
  9. 2026Adaptive deep nonparametric regression from dependent data under covariate shiftcited by 0