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 $\mathcal{O}(n^{-1/\alpha})$, for all $\alpha > 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.

翻译：在本文中,我们执行深层神经网络以学习 $\ psi$ 微弱依赖性进程。这种脆弱依赖性属性包括一系列薄弱的依赖性条件,如混合、关联、$\ cdotts$和此处所考虑的设置包括许多常用情况,如:回归估计、时间序列预测、时间序列分类、$\ cdots$等。在深神经网络预测器类中,经验风险最小化算法的一致性得到确立。我们实现了普遍性约束并获得了学习率,对于所有 $\mathcal{O}(n ⁇ -1/\ alpha}) 来说,学习率低于$\ alpha > 2 $。应用了与外源共产物结合的亲因模型的二元时间序列分类和预测。提供了一些模拟结果,以及美国衰退数据的应用。