Study Analyzes Convergence Speed of Data-Augmentation Gibbs Samplers for Bayesian Probit Regression
Researchers have derived explicit, non-asymptotic bounds on the mixing times of data-augmentation Gibbs samplers used in Bayesian probit regression, valid in high-dimensional settings where both data points and parameters are large. The bounds depend on the design matrix and prior precision and are shown to be tight in the worst case over response vectors. The results offer principled guidance for choosing prior distributions that guarantee fast sampler convergence, with practical relevance for large-scale Bayesian computation.
A new preprint on arXiv presents a theoretical analysis of data-augmentation Gibbs samplers commonly used for Bayesian probit regression, a workhorse model in binary classification. By leveraging recent advances in the study of Gibbs samplers for log-concave targets, the authors derive simple, explicit non-asymptotic mixing time bounds expressed in Kullback-Leibler divergence. Crucially, the bounds hold uniformly over all response vectors and depend explicitly on the design matrix and prior precision, making them interpretable and actionable. The paper identifies distinct high-dimensional regimes—where both the number of observations n and parameters p grow large—in which mixing times either remain bounded or diverge, clarifying when these popular samplers are computationally reliable. The bounds are proven tight in the worst case with respect to responses, lending them theoretical credibility. An empirical study using coupling techniques further validates that the bounds accurately predict practically observed mixing behavior, bridging theory and practice.
What's missing
The paper is a preprint and has not yet undergone formal peer review. It is unclear whether the theoretical guarantees extend to related data-augmentation schemes beyond the specific probit regression samplers analyzed, or to non-log-concave posterior targets.
What different sources said
- arXiv stat.MLCenter
Mixing times of data-augmentation Gibbs samplers for high-dimensional probit regression
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