Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
- We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process.
| Author details: | Gilles BlanchardGND, Oleksandr Zadorozhnyi |
|---|---|
| DOI: | https://doi.org/10.3150/18-BEJ1095 |
| ISSN: | 1350-7265 |
| ISSN: | 1573-9759 |
| Title of parent work (English): | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
| Publisher: | International Statistical Institute |
| Place of publishing: | Voorburg |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/09/25 |
| Publication year: | 2019 |
| Release date: | 2020/10/20 |
| Tag: | Banach-valued process; Bernstein inequality; concentration; spectral regularization; weak dependence |
| Volume: | 25 |
| Issue: | 4B |
| Number of pages: | 38 |
| First page: | 3421 |
| Last Page: | 3458 |
| Funding institution: | DFGGerman Research Foundation (DFG) [CRC-1294, FOR-1735] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| Open Access / Green Open-Access |
