Kernel regression, minimax rates and effective dimensionality
- We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales.
| Author details: | Gilles BlanchardORCiDGND, Nicole MückeORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1142/S0219530519500258 |
| ISSN: | 0219-5305 |
| ISSN: | 1793-6861 |
| Title of parent work (English): | Analysis and applications |
| Subtitle (English): | beyond the regular case |
| Publisher: | World Scientific |
| Place of publishing: | New Jersey |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/02/11 |
| Publication year: | 2020 |
| Release date: | 2023/03/21 |
| Tag: | Kernel regression; eigenvalue decay; minimax optimality |
| Volume: | 18 |
| Issue: | 4 |
| Number of pages: | 14 |
| First page: | 683 |
| Last Page: | 696 |
| Funding institution: | German Research Foundation under DFGGerman Research Foundation (DFG); [STE 1074/4-1] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
