Mixing Time Bounds for the Gibbs Sampler under Isoperimetry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915959961288704 |
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| author | Goyal, Alexander Deligiannidis, George Kantas, Nikolas |
| author_facet | Goyal, Alexander Deligiannidis, George Kantas, Nikolas |
| contents | We establish bounds on the conductance for the systematic-scan and random-scan Gibbs samplers when the target distribution satisfies a Poincaré or log-Sobolev inequality and possesses sufficiently regular conditional distributions. These bounds lead to mixing time guarantees that extend beyond the log-concave setting, offering new insights into the convergence behavior of Gibbs sampling in broader regimes. Moreover, we demonstrate that our results remain valid for log-Lipschitz and log-smooth target distributions. Our approach relies on novel isoperimetric inequalities and a sequential coupling argument for the Gibbs sampler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing Time Bounds for the Gibbs Sampler under Isoperimetry Goyal, Alexander Deligiannidis, George Kantas, Nikolas Statistics Theory Probability We establish bounds on the conductance for the systematic-scan and random-scan Gibbs samplers when the target distribution satisfies a Poincaré or log-Sobolev inequality and possesses sufficiently regular conditional distributions. These bounds lead to mixing time guarantees that extend beyond the log-concave setting, offering new insights into the convergence behavior of Gibbs sampling in broader regimes. Moreover, we demonstrate that our results remain valid for log-Lipschitz and log-smooth target distributions. Our approach relies on novel isoperimetric inequalities and a sequential coupling argument for the Gibbs sampler. |
| title | Mixing Time Bounds for the Gibbs Sampler under Isoperimetry |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2506.22258 |