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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 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.

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Author:Luc Bonnet, Jean-Luc Akian, Éric Savin, T. J. Sullivan
Document Type:Article
Parent Title (English):Algorithms
First Page:196
Year of first publication:2020
ArXiv Id:http://arxiv.org/abs/2007.05236
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