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