Sparse-penalized deep neural networks estimator under weak dependence

William Kengne () and Modou Wade ()
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William Kengne: Université Jean Monnet, ICJ UMR5208, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1
Modou Wade: THEMA, CY Cergy Paris Université

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 4, No 3, 469-500

Abstract: Abstract We consider the nonparametric regression and the classification problems for $$\psi $$ ψ -weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association $$\cdots $$ ⋯ A penalized estimation method for sparse deep neural networks is performed. In both nonparametric regression and binary classification problems, we establish oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators. Convergence rates of the excess risk of these estimators are also derived. The simulation results displayed show that, the proposed estimators can work well than the non penalized estimators, and that, there is a gain of using this estimator.

Keywords: Deep neural network; $$\psi $$ ψ -Weakly dependence; Sparsity; Penalization; Convergence rate; 62M45; 62M10; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00965-1

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