# Deep learning for psi-weakly dependent processes

arXiv: https://arxiv.org/abs/2302.00333 · HTML: https://mlsanity.com/paper/2302.00333/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [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)
- [Generalization bounds for deep learning](https://mlsanity.com/paper/2012.04115/) (2020)
- [Smooth function approximation by deep neural networks with general activation functions](https://mlsanity.com/paper/1906.06903/) (2019)
- [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)
- [Adaptive deep learning for nonlinear time series models](https://mlsanity.com/paper/2207.02546/) (2022)

## Built on by (most cited first, 2 of 2)

- [Sparse-penalized deep neural networks estimator under weak dependence](https://mlsanity.com/paper/2303.01406/) (2023)
- [Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approach](https://mlsanity.com/paper/2401.08978/) (2024)

## Abstract (arXiv)

In this paper, we perform deep neural networks for learning psi-weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association,cdots and the setting considered here covers many commonly used situations such as: regression estimation, time series prediction, time series classification,cdots The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. We achieve the generalization bound and obtain a learning rate, which is less than O(n-1/α), for all α > 2 . Applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. Some simulation results are provided, as well as an application to the US recession data.