Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes
- In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.
Author details: | Mariantonia CotroneiORCiD, Rosa Di SalvoORCiD, Matthias HolschneiderORCiDGND, Luigia PuccioORCiD |
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DOI: | https://doi.org/10.1016/j.cam.2016.08.002 |
ISSN: | 0377-0427 |
ISSN: | 1879-1778 |
Title of parent work (English): | Journal of computational and applied mathematics |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Date of first publication: | 2016/08/27 |
Publication year: | 2017 |
Release date: | 2022/07/04 |
Tag: | Bayesian inversion; Interpolation; Simulation of Gaussian processes; Subdivision schemes |
Volume: | 311 |
Number of pages: | 12 |
First page: | 342 |
Last Page: | 353 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |