Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification
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 sta...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/13/8/196 |
| _version_ | 1797558404519034880 |
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| author | Luc Bonnet Jean-Luc Akian Éric Savin T. J. Sullivan |
| author_facet | Luc Bonnet Jean-Luc Akian Éric Savin T. J. Sullivan |
| author_sort | Luc Bonnet |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T17:30:00Z |
| format | Article |
| id | doaj.art-be3357bf68734a6bacc7f5816c0bb63c |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T17:30:00Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-be3357bf68734a6bacc7f5816c0bb63c2023-11-20T10:03:36ZengMDPI AGAlgorithms1999-48932020-08-0113819610.3390/a13080196Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty QuantificationLuc Bonnet0Jean-Luc Akian1Éric Savin2T. J. Sullivan3ONERA, 29 Avenue de la Division Leclerc, 92320 Châtillon, FranceONERA, 29 Avenue de la Division Leclerc, 92320 Châtillon, FranceONERA, 29 Avenue de la Division Leclerc, 92320 Châtillon, FranceMathematics Institute and School of Engineering, University of Warwick, Coventry CV4 7AL, UKMotivated 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.https://www.mdpi.com/1999-4893/13/8/196adaptive approximationisotonic regressionoptimisation under uncertaintyuncertainty quantificationaerodynamic design |
| spellingShingle | Luc Bonnet Jean-Luc Akian Éric Savin T. J. Sullivan Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification Algorithms adaptive approximation isotonic regression optimisation under uncertainty uncertainty quantification aerodynamic design |
| title | Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification |
| title_full | Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification |
| title_fullStr | Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification |
| title_full_unstemmed | Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification |
| title_short | Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification |
| title_sort | adaptive reconstruction of imperfectly observed monotone functions with applications to uncertainty quantification |
| topic | adaptive approximation isotonic regression optimisation under uncertainty uncertainty quantification aerodynamic design |
| url | https://www.mdpi.com/1999-4893/13/8/196 |
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