# Sparse-penalized deep neural networks estimator under weak dependence

arXiv: https://arxiv.org/abs/2303.01406 · HTML: https://mlsanity.com/paper/2303.01406/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [Smooth function approximation by deep neural networks with general activation functions](https://mlsanity.com/paper/1906.06903/) (2019)
- [Nonconvex sparse regularization for deep neural networks and its optimality](https://mlsanity.com/paper/2003.11769/) (2020)
- [On the Inductive Bias of Dropout](https://mlsanity.com/paper/1412.4736/) (2014)
- [Advantage of Deep Neural Networks for Estimating Functions with Singularity on Hypersurfaces](https://mlsanity.com/paper/2011.02256/) (2020)
- [Theoretical analysis of deep neural networks for temporally dependent observations](https://mlsanity.com/paper/2210.11530/) (2022)
- [On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data](https://mlsanity.com/paper/2011.00328/) (2020)
- [Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space](https://mlsanity.com/paper/2009.11285/) (2020)
- [Excess risk bound for deep learning under weak dependence](https://mlsanity.com/paper/2302.07503/) (2023)
- [Deep learning for psi-weakly dependent processes](https://mlsanity.com/paper/2302.00333/) (2023)

## Built on by (most cited first, 8 of 8)

- [Implicit Compressibility of Overparametrized Neural Networks Trained with Heavy-Tailed SGD](https://mlsanity.com/paper/2306.08125/) (2023)
- [Robust deep learning from weakly dependent data](https://mlsanity.com/paper/2405.05081/) (2024)
- [Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds](https://mlsanity.com/paper/2410.21702/) (2024)
- [Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approach](https://mlsanity.com/paper/2401.08978/) (2024)
- [Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax optimality](https://mlsanity.com/paper/2406.08321/) (2024)
- [Penalized deep neural networks estimator with general loss functions under weak dependence](https://mlsanity.com/paper/2305.06230/) (2023)
- [A general framework for deep learning](https://mlsanity.com/paper/2512.23425/) (2025)
- [Prediction Inference of Time Series with Standard ReLU Deep Neural Networks](https://mlsanity.com/paper/2608.15362/) (2026)

## Abstract (arXiv)

We consider the nonparametric regression and the classification problems for psi-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, ldots. A penalized estimation method for sparse deep neural networks is performed. In both nonparametric regression and binary classification problems, we establish oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators. Convergence rates of the excess risk of these estimators are also derived. The simulation results displayed show that, the proposed estimators overall work well than the non penalized estimators.