Sparse-penalized deep neural networks estimator under weak dependence
This work addresses regression and classification problems for weakly dependent data, which is more general than common assumptions like mixing, but it appears incremental as it extends existing sparse neural network methods to this broader dependency context.
The authors tackled nonparametric regression and classification for weakly dependent processes by developing a penalized estimation method for sparse deep neural networks, establishing oracle inequalities and convergence rates for the excess risk, with simulation results showing the proposed estimators outperform non-penalized ones.
We consider the nonparametric regression and the classification problems for $ψ$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. 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 overall work well than the non penalized estimators.