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Adaptive reconstruction of imperfectly observed monotone functions, with applications to uncertainty quantification
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Bonnet, Luc, Akian, Jean-Luc, Savin, Éric and Sullivan, Tim J. (2020) Adaptive reconstruction of imperfectly observed monotone functions, with applications to uncertainty quantification. Algorithms, 13 (8). e196. doi:10.3390/a13080196 ISSN 1999-4893.
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Official URL: https://doi.org/10.3390/a13080196
Abstract
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Probabilities, Approximation theory , Regression analysis, Mathematical optimization | ||||||
Journal or Publication Title: | Algorithms | ||||||
Publisher: | MDPI | ||||||
ISSN: | 1999-4893 | ||||||
Official Date: | 13 August 2020 | ||||||
Dates: |
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Volume: | 13 | ||||||
Number: | 8 | ||||||
Article Number: | e196 | ||||||
DOI: | 10.3390/a13080196 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 4 September 2020 | ||||||
Date of first compliant Open Access: | 7 September 2020 | ||||||
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