Year: 2026
Type: preprint
Abstract: Split Gibbs sampling (SGS) is a versatile tool to sample from complex posterior distributions, such as those arising in imaging inverse problems. However, existing SGS instances are limited to quadratic variable couplings, restricting their applicability to Gaussian likelihoods. This letter genearalizes SGS to non-Euclidean geometry by introducing a coupling kernel defined through a Jensen-Bregman divergence. This framework not only enables posterior sampling in these settings but also unifies several \emph{ad hoc} sampling schemes from the literature under a principled theoretical foundation.
Source: arXiv (Cornell University)
Institutions: Institut National Polytechnique de Toulouse, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay, CEA Paris-Saclay - Etablissement de Saclay, Laboratoire d'Intégration des Systèmes et des Technologies, Institut de Recherche en Informatique de Toulouse, École Nationale Supérieure d'Électrotechnique, d'Électronique, d'Informatique, d'Hydraulique et des Télécommunications, Université de Rouen Normandie
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7221820249