Title : Deep learning for $\psi$-weakly dependent processes

Abstract : In this paper, we perform deep neural networks for learning stationary $\psi$-wealy dependent processes. Such weak dependent structure is more general the condition such as
mixing, association… and the setting that we consider covers commonly used situation such as: regression estimation, time series prediction, time series classification… We evaluate the consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors. We drive generalization error bound and obtain a learning rate, which is less than $O(n^{-1/\alpha})$, for all $\alpha > 2$. Applications to binary classification and prediction in affine causal models with exogenous covariates are carried out.