Certified coordinate selection for high-dimensional Bayesian inversion with Laplace prior - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Certified coordinate selection for high-dimensional Bayesian inversion with Laplace prior

Résumé

We consider high-dimensional Bayesian inverse problems with arbitrary likelihood and product-form Laplace prior for which we provide a certified approximation of the posterior density in the Hellinger distance. The approximate posterior density differs from the prior density only in a small number of relevant coordinates that contribute the most to the update from the prior to the posterior. We propose and analyze a gradient-based diagnostic to identify these relevant coordinates. Although this diagnostic requires computing an expectation with respect to the posterior, we propose tractable methods for the classical case of a linear forward model with Gaussian likelihood. Our methods can be employed to estimate the diagnostic before solving the Bayesian inverse problem via, e.g., Markov chain Monte Carlo (MCMC) methods. After selecting the coordinates, the approximate posterior density can be efficiently inferred since most of its coordinates are only informed by the prior. Moreover, specialized MCMC methods, such as the pseudo-marginal MCMC algorithm, can be used to obtain less correlated samples when sampling the exact posterior density. We show the applicability of our method using a 1D signal deblurring problem and a high-dimensional 2D super-resolution problem.

Dates et versions

hal-04273681 , version 1 (07-11-2023)

Licence

Paternité

Identifiants

Citer

Rafael Flock, Yiqiu Dong, Felipe Uribe, Olivier Zahm. Certified coordinate selection for high-dimensional Bayesian inversion with Laplace prior. 2023. ⟨hal-04273681⟩
25 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More