Back to Search
Start Over
Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces.
- Source :
-
Applied & Computational Harmonic Analysis . May2020, Vol. 48 Issue 3, p868-890. 23p. - Publication Year :
- 2020
-
Abstract
- In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regression, principal component regression, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*RATES
Subjects
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 48
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 141918651
- Full Text :
- https://doi.org/10.1016/j.acha.2018.09.009