Certified dimension reduction of the input parameter space of Bayesian inverse problems

Olivier Zahm 1 Youssef Marzouk 2 Clémentine Prieur 1 Paul Constantine 3
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : Approximation of multivariate functions is a difficult task when the number of input parameters is large. Identifying the directions where the function does not significantly vary is a key preprocessing step to reduce the complexity of the approximation algorithms. In [1] we propose a gradient-based method that permits to detect such a low-dimensional structure of a function. Our methodology consists in minimizing an upper-bound of the approximation error obtained using Poincaré-type inequalities, and it generalizes the Active Subspace method [2]. Numerical examples reveal the importance of the choice of the metric to measure errors and compare it with the commonly used truncated Karhunen– Loève decomposition.
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Conference papers
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https://hal.inria.fr/hal-01955800
Contributor : Olivier Zahm <>
Submitted on : Friday, December 14, 2018 - 3:58:30 PM
Last modification on : Friday, July 26, 2019 - 1:44:05 PM

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Olivier Zahm, Youssef Marzouk, Clémentine Prieur, Paul Constantine. Certified dimension reduction of the input parameter space of Bayesian inverse problems. IMS 2018 - 12th International Vilnius Conference on Probability Theory and Mathematical Statistics, Jul 2018, Vilnius, Lithuania. ⟨hal-01955800⟩

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