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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2409.17991 |
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| _version_ | 1866917787616673792 |
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| author | Lerma-Pineda, Andres Felipe Petersen, Philipp Frieder, Simon Lukasiewicz, Thomas |
| author_facet | Lerma-Pineda, Andres Felipe Petersen, Philipp Frieder, Simon Lukasiewicz, Thomas |
| contents | We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every $RBV^2$ function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. And we leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension-independent learning rates for high-dimensional classification problems Lerma-Pineda, Andres Felipe Petersen, Philipp Frieder, Simon Lukasiewicz, Thomas Machine Learning Numerical Analysis 68T05, 62C20, 41A25, 41A46 We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every $RBV^2$ function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. And we leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries. |
| title | Dimension-independent learning rates for high-dimensional classification problems |
| topic | Machine Learning Numerical Analysis 68T05, 62C20, 41A25, 41A46 |
| url | https://arxiv.org/abs/2409.17991 |