mlsanityData to 7 Oct 2026

Statistical learning by sparse deep neural networks

arXiv 2311.08845 ↗First posted 15 Nov 2023math.ST cs.LG stat.MEcited by 1

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Abstract (arXiv)

We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively nearly-minimax (up to log-factors) simultaneously across the entire range of various function classes.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 17 of its 33 references that are in the map. First posted on arXiv 15 Nov 2023.

Builds on

17 of 33 references.

References · 17

  1. 2016Error bounds for approximations with deep ReLU networkscited by 567
  2. 2016Learning Structured Sparsity in Deep Neural Networkscited by 538
  3. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  4. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  5. 2017Size-Independent Sample Complexity of Neural Networkscited by 289
  6. 2021Deep learning: a statistical viewpointcited by 239
  7. 2018Optimal approximation of continuous functions by very deep ReLU networkscited by 165
  8. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
  9. 2015Provable approximation properties for deep neural networkscited by 60
  10. 2018Fast convergence rates of deep neural networks for classificationcited by 46
  11. 2020Expressivity of Deep Neural Networkscited by 31
  12. 2020Statistical Guarantees for Regularized Neural Networkscited by 25
5 more
  1. 2020Nonconvex sparse regularization for deep neural networks and its optimalitycited by 21
  2. 2017High-dimensional classification by sparse logistic regressioncited by 19
  3. 2020Advantage of Deep Neural Networks for Estimating Functions with Singularity on Hypersurfacescited by 17
  4. 2022Statistical guarantees for sparse deep learningcited by 9
  5. 2022Upper bounds on the Natarajan dimensions of some function classescited by 8

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Citing papers per year: 2024: 1.

1 paper.

  1. 2024Sparse deep neural networks for nonparametric estimation in high-dimensional sparse regressioncited by 0