Penalized deep neural networks estimator with general loss functions under weak dependence

2023/05/10 by William Kengne, Kengne, William, Modou Wade +1
Computer Science · Engineering · Mathematics · #Energy Load and Power Forecasting #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2305.06230

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, ⋯ The ψ-weak dependence structure is considered, and for the specific case of bounded observations, θ_∞-coefficients are also used. In this case of θ_∞-weakly dependent, a non asymptotic generalization bound within the class of deep neural networks predictors is provided. For learning both ψ and θ_∞-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 O(n^-1/3). Some simulation results are provided, and application to the forecast of the particulate matter in the Vitória metropolitan area is also considered.

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