Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems
- In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.
| Author details: | Abhishake RastogiORCiD |
|---|---|
| DOI: | https://doi.org/10.1063/1.5136221 |
| ISBN: | 978-0-7354-1930-8 |
| ISSN: | 0094-243X |
| Title of parent work (English): | AIP Conference Proceedings : third international Conference of mathematical sciences (ICMS 2019) |
| Publisher: | American Institute of Physics |
| Place of publishing: | Melville |
| Publication type: | Other |
| Language: | English |
| Year of first publication: | 2019 |
| Publication year: | 2019 |
| Release date: | 2021/04/26 |
| Tag: | Hilbert Scales; Minimax convergence rates; Reproducing kernel Hilbert space; Statistical inverse problem; Tikhonov regularization |
| Volume: | 2183 |
| Number of pages: | 4 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1294] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
