Related papers: Deep learning for $\psi$-weakly dependent processes

Deep learning for $\psi$-weakly dependent processes

URL: http://arxiv.org/abs/2302.00333v1
Date: Wed, 1 Feb 2023 09:31:15 GMT
Title: Deep learning for $\psi$-weakly dependent processes
Authors: William Kengne, Wade Modou
Abstract summary: We perform deep neural networks for learning $psi$-weakly dependent processes. The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. Some simulation results are provided, as well as an application to the US recession data.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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