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Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems

Tiangang Cui 1 Olivier Zahm 2
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based dimension reduction method in which the informed subspace does not depend on the data. This permits online-offline computational strategy where the expensive low-dimensional structure of the problem is detected in an offline phase, meaning before observing the data. This strategy is particularly relevant for multiple inversion problems as the same informed subspace can be reused. The proposed approach allows to control the approximation error (in expectation over the data) of the posterior distribution. We also present sampling strategies which exploit the informed subspace to draw efficiently samples from the exact posterior distribution. The method is successfully illustrated on two numerical examples: a PDE-based inverse problem and a tomography problem with Poisson data.
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https://hal.inria.fr/hal-02938064
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Submitted on : Monday, September 14, 2020 - 4:32:09 PM
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Tiangang Cui, Olivier Zahm. Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems. 2020. ⟨hal-02938064⟩

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