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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.00417 |
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| _version_ | 1866909748077527040 |
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| author | Durmus, Alain Gruffaz, Samuel Hasenpflug, Mareike Rudolf, Daniel |
| author_facet | Durmus, Alain Gruffaz, Samuel Hasenpflug, Mareike Rudolf, Daniel |
| contents | We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) 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, is reversible with respect to the distribution of interest, and generalizes Hit-and-run slice sampling on $\mathbb{R}^{d}$ to Riemannian manifolds by using geodesics instead of straight lines. We demonstrate the robustness of our sampler's performance compared to other MCMC methods dealing with manifold valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate its remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00417 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geodesic slice sampling on Riemannian manifolds Durmus, Alain Gruffaz, Samuel Hasenpflug, Mareike Rudolf, Daniel Computation Probability Applications 60-08 G.3 We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) 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, is reversible with respect to the distribution of interest, and generalizes Hit-and-run slice sampling on $\mathbb{R}^{d}$ to Riemannian manifolds by using geodesics instead of straight lines. We demonstrate the robustness of our sampler's performance compared to other MCMC methods dealing with manifold valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate its remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning. |
| title | Geodesic slice sampling on Riemannian manifolds |
| topic | Computation Probability Applications 60-08 G.3 |
| url | https://arxiv.org/abs/2312.00417 |