Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference

• URL: http://arxiv.org/abs/2602.22369v1
• Date: Wed, 25 Feb 2026 20:06:07 GMT
• Title: Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference
• Authors: Ruixiao Wang, Xiaohong Chen, Sinho Chewi,
• Abstract summary: We show that in a pre-asymptotic'' regime, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode.<n>We provide a non-asymptotic sampling guarantee by analyzing the spectral gap of Langevin dynamics.
• Score: 10.581650211628213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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