# Statistical learning by sparse deep neural networks

arXiv: https://arxiv.org/abs/2311.08845 · HTML: https://mlsanity.com/paper/2311.08845/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Provable approximation properties for deep neural networks](https://mlsanity.com/paper/1509.07385/) (2015)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [Expressivity of Deep Neural Networks](https://mlsanity.com/paper/2007.04759/) (2020)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Nonconvex sparse regularization for deep neural networks and its optimality](https://mlsanity.com/paper/2003.11769/) (2020)
- [High-dimensional classification by sparse logistic regression](https://mlsanity.com/paper/1706.08344/) (2017)
- [Advantage of Deep Neural Networks for Estimating Functions with Singularity on Hypersurfaces](https://mlsanity.com/paper/2011.02256/) (2020)
- [Statistical guarantees for sparse deep learning](https://mlsanity.com/paper/2212.05427/) (2022)
- [Upper bounds on the Natarajan dimensions of some function classes](https://mlsanity.com/paper/2209.07015/) (2022)

## Built on by (most cited first, 1 of 1)

- [Sparse deep neural networks for nonparametric estimation in high-dimensional sparse regression](https://mlsanity.com/paper/2406.18137/) (2024)

## 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.