This paper carries out sparse-penalized deep neural networks predictors for learning weakly dependent processes, with a broad class of loss functions. We deal with a general framework that includes, regression estimation, classification, times series prediction, $\cdots$ The $\psi$-weak dependence structure is considered, and for the specific case of bounded observations, $\theta_\infty$-coefficients are also used. In this case of $\theta_\infty$-weakly dependent, a non asymptotic generalization bound within the class of deep neural networks predictors is provided. For learning both $\psi$ and $\theta_\infty$-weakly dependent processes, oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators are established. When the target function is sufficiently smooth, the convergence rate of these excess risk is close to $\mathcal{O}(n^{-1/3})$. Some simulation results are provided, and application to the forecast of the particulate matter in the Vit\'{o}ria metropolitan area is also considered.

翻译：本文针对弱相依过程的学习，采用稀疏惩罚深度神经网络预测器，并涵盖广泛的损失函数类别。我们处理了一个通用框架，包括回归估计、分类、时间序列预测等。考虑了ψ-弱相依结构，并在有界观测的特殊情况下，同时使用了θ∞系数。对于θ∞-弱相依情形，我们给出了深度神经网络预测器类别内的非渐近泛化界。为学习ψ和θ∞-弱相依过程，建立了稀疏惩罚深度神经网络估计器超额风险的神谕不等式。当目标函数足够光滑时，这些超额风险的收敛速率接近O(n^{-1/3})。本文提供了部分仿真结果，并考虑了在维多利亚大都市区颗粒物预测中的应用。