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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08321 |
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Table of Contents:
- 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,$\cdots$, 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 $L_2$ 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 $L_2$ 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.