Excess risk bound for deep learning under weak dependence

2023/02/15 by William Kengne, Kengne, William · 1 citation
Computer Science · Mathematics · #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Healthcare #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2302.07503

openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The ψ-weak dependence structure considered is quite large and covers other conditions such as mixing, association,… Firstly, the approximation of smooth functions by deep neural networks with a broad class of activation functions is considered. We derive the required depth, width and sparsity of a deep neural network to approximate any Hölder smooth function, defined on any compact set \mx. Secondly, we establish a bound of the excess risk for the learning of weakly dependent observations by deep neural networks. When the target function is sufficiently smooth, this bound is close to the usual O(n^-1/2).

Cited by

• A general framework for deep learning

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• Deep learning for ψ-weakly dependent processes
• Penalized deep neural networks estimator with general loss functions under weak dependence
• Robust deep learning from weakly dependent data
• Sparse-penalized deep neural networks estimator under weak dependence
• Statistical learning for ψ-weakly dependent processes