HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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 with a Gaussian process prior and a tomography problem with Poisson data and a Besov-$\mathcal{B}^2_{11}$ prior.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Contributor : Olivier Zahm Connect in order to contact the contributor
Submitted on : Monday, March 1, 2021 - 9:11:56 AM
Last modification on : Friday, February 4, 2022 - 3:21:30 AM


Files produced by the author(s)


  • HAL Id : hal-02938064, version 2
  • ARXIV : 2102.13245



Tiangang Cui, Olivier Zahm. Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems. 2021. ⟨hal-02938064v2⟩



Record views


Files downloads