SRI - Center for Uncertainty Quantification
in Computational Science & Engineering
Home
About
People
Faculty
Visiting Professors
Consultants
Research Scientists
Postdoctoral Fellows
Students
Visiting Students
Staff
Member of the Board
Previous Members
Research
Research Projects
Posters
Publications
Books
Book Chapters
Conference Proceedings
Manuscripts
Refereed Journals
Technical Reports
Events
Calendar
Gallery
KAUST UQ School 2016
Zavala's Seminar and Short Course
Grossmann’s Seminars and Short Course
UQ Annual Workshop 2016
UQ Annual Workshop 2015
Spatial Statistics Workshop 2014
UQ Annual Workshop 2014
UQ Annual Workshop 2013
News
Courses
Spring 2016
Summer 2015
Fall 2015
Seminars
Join Us
Links
Home
>
Publications
>
Manuscripts
>
Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations in random points
Publications
Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations in random points
Bibliography:
Bibliography
G. Migliorati, F. Nobile, R. Tempone,
Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations in random points
,
Journal of Multivariate Analysis, Vol. 142, Pages 167–182. December 2015.
Authors:
G. Migliorati, F. Nobile, R. Tempone
Keywords:
approximation theory, discrete least squares, noisy evaluations, error analysis, convergence rates, large deviations, learning theory, multivariate polynomial approximation
Year:
2015
Abstract:
We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. The convergence estimates are given in mean-square sense with respect to the sampling measure. The noise may be correlated with the location of the evaluation and may have nonzero mean (offset). We consider both cases of bounded or square-integrable noise / offset. We prove conditions between the number of sampling points and the dimension of the underlying approximation space that ensure a stable and accurate approximation. Particular focus is on deriving estimates in probability within a given confidence level. We analyze how the best approximation error and the noise terms affect the convergence rate and the overall confidence level achieved by the convergence estimate. The proofs of our convergence estimates in probability use arguments from the theory of large deviations to bound the noise term. Finally we address the particular case of multivariate polynomial approximation spaces with any density in the beta family, including uniform and Chebyshev.
ISSN:
2015
http://mathicse.epfl.ch/files/content/sites/mathicse/files/Mathicse%20reports%202015/03-2015_GM-FN-RT%20NEW.pdf
No
Site Map
|
Privacy Policy
|
Terms of Use
|
Team Site
©
2021
King Abdullah University of Science and Technology,
All rights reserved.
SRI - Center for Uncertainty Quantification
in Computational Science & Engineering
http://
http://