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.

本文使用稀疏惩罚深度神经网络预测器来学习弱相关过程，并提供了深度神经网络预测器类中θ∞-coefficients 弱相关的非渐进泛化界限和超额风险的奥拉克不等式。

弱相依下通用损失函数的惩罚深度神经网络估计器