Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911469505871872 |
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| author | Wang, Ruixiao Chen, Xiaohong Chewi, Sinho |
| author_facet | Wang, Ruixiao Chen, Xiaohong Chewi, Sinho |
| contents | This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as the non-regular part of the model. We show that in a ``pre-asymptotic'' regime in which the limiting Laplace approximation is not yet valid, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode. Within this region, the distribution is a bounded perturbation of a product measure: a strongly log-concave distribution in the regular part and a one-dimensional exponential-type distribution in each coordinate of the non-regular part. Leveraging this structure, we provide a non-asymptotic sampling guarantee by analyzing the spectral gap of Langevin dynamics. Key examples of low-temperature Gibbs distributions include Bayesian posteriors, and we demonstrate our results on three canonical examples: a high-dimensional logistic regression model, a Poisson linear model, and a Gaussian mixture model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_22369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference Wang, Ruixiao Chen, Xiaohong Chewi, Sinho Statistics Theory Probability Machine Learning This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as the non-regular part of the model. We show that in a ``pre-asymptotic'' regime in which the limiting Laplace approximation is not yet valid, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode. Within this region, the distribution is a bounded perturbation of a product measure: a strongly log-concave distribution in the regular part and a one-dimensional exponential-type distribution in each coordinate of the non-regular part. Leveraging this structure, we provide a non-asymptotic sampling guarantee by analyzing the spectral gap of Langevin dynamics. Key examples of low-temperature Gibbs distributions include Bayesian posteriors, and we demonstrate our results on three canonical examples: a high-dimensional logistic regression model, a Poisson linear model, and a Gaussian mixture model. |
| title | Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference |
| topic | Statistics Theory Probability Machine Learning |
| url | https://arxiv.org/abs/2602.22369 |