Geodesic slice sampling on Riemannian manifolds

• 成果类型: Article
• 署名作者: Durmus, Alain; Gruffaz, Samuel; Hasenpflug, Mareike; Rudolf, Daniel
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; Universite Paris Cite; University of Passau
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag006
• 发表日期: 2026
• 页码: asag006
• 关键词: Grassmann manifold; Markov Chain Monte Carlo; Riemannian manifold; Slice sampling; Stiefel manifold; monte-carlo; CONVERGENCE; statistics; geometry

摘要

We propose a theoretically justified and practically applicable slice-sampling-based Markov chain Monte Carlo method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior distributions in Bayesian inference of matrix-valued parameters, for example belonging to either the Stiefel or the Grassmann manifold. Our method, called geodesic slice sampling, generalizes hit-and-run slice sampling on $ \mathbb{R}<^>{d} $ to Riemannian manifolds by abstracting straight lines to geodesics. It is reversible with respect to the distribution of interest and converges to the latter in total variation distance. We demonstrate the robustness of our sampler's performance compared to other Markov chain Monte Carlo methods dealing with manifold-valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate the sampler's remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning.