On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917976599429120 |
|---|---|
| author | Kohler, Michael |
| author_facet | Kohler, Michael |
| contents | Nonparametric regression with random design is considered.
The $L_2$ error with integration with respect to the design
measure is used as the error criterion.
An over-parametrized deep neural network
regression estimate
with logistic activation function
is defined, where all weights are learned
by gradient descent. It is shown that the estimate
achieves a nearly optimal rate of convergence in case
that the regression function is $(p,C)$--smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent Kohler, Michael Statistics Theory Nonparametric regression with random design is considered. The $L_2$ error with integration with respect to the design measure is used as the error criterion. An over-parametrized deep neural network regression estimate with logistic activation function is defined, where all weights are learned by gradient descent. It is shown that the estimate achieves a nearly optimal rate of convergence in case that the regression function is $(p,C)$--smooth. |
| title | On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2504.03405 |