On the kernel learning problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908398340014080 |
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| author | Li, Yang Ruan, Feng |
| author_facet | Li, Yang Ruan, Feng |
| contents | The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space. Here we consider a generalization of the kernel ridge regression problem, by introducing an extra matrix parameter $U$, which aims to detect the scale parameters and the feature variables in the data, and thereby improve the efficiency of kernel ridge regression. This naturally leads to a nonlinear variational problem to optimize the choice of $U$. We study various foundational mathematical aspects of this variational problem, and in particular how this behaves in the presence of multiscale structures in the data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the kernel learning problem Li, Yang Ruan, Feng Machine Learning Classical Analysis and ODEs Functional Analysis Optimization and Control The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space. Here we consider a generalization of the kernel ridge regression problem, by introducing an extra matrix parameter $U$, which aims to detect the scale parameters and the feature variables in the data, and thereby improve the efficiency of kernel ridge regression. This naturally leads to a nonlinear variational problem to optimize the choice of $U$. We study various foundational mathematical aspects of this variational problem, and in particular how this behaves in the presence of multiscale structures in the data. |
| title | On the kernel learning problem |
| topic | Machine Learning Classical Analysis and ODEs Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2502.11665 |