2024/06/12 by Kengne, William, Wade, Modou · 1 citation
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · doi:10.48550/arxiv.2406.08321
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out deep learning from strongly mixing observations, and deal with the squared and a broad class of loss functions. We consider sparse-penalized regularization for deep neural network predictor. For a general framework that includes, regression estimation, classification, time series prediction,⋯, oracle inequality for the expected excess risk is established and a bound on the class of Hölder smooth functions is provided. For nonparametric regression from strong mixing data and sub-exponentially error, we provide an oracle inequality for the L2 error and investigate an upper bound of this error on a class of Hölder composition functions. For the specific case of nonparametric autoregression with Gaussian and Laplace errors, a lower bound of the L2 error on this Hölder composition class is established. Up to logarithmic factor, this bound matches its upper bound; so, the deep neural network estimator attains the minimax optimal rate.