1. Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification
- Author
-
Bonnet, L., Akian, J. -L., Savin, É., and Sullivan, T. J.
- Subjects
Mathematics - Numerical Analysis ,Mathematics - Optimization and Control ,Statistics - Other Statistics ,49M30, 62G08, 68T37 - 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., Comment: 19 pages, 10 figures. This is a preprint version of an article to appear in Algorithms and differs from the publisher's final version in layout and typographical detail
- Published
- 2020
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