# Mixing times of data-augmentation Gibbs samplers for high-dimensional probit regression

arXiv: https://arxiv.org/abs/2505.14343 · HTML: https://mlsanity.com/paper/2505.14343/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 53 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 16 of 16)

- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling](https://mlsanity.com/paper/2109.13055/) (2021)
- [Penalising model component complexity: A principled, practical approach to constructing priors](https://mlsanity.com/paper/1403.4630/) (2014)
- [Conjugate Bayes for probit regression via unified skew-normal distributions](https://mlsanity.com/paper/1802.09565/) (2018)
- [Estimating Convergence of Markov chains with L-Lag Couplings](https://mlsanity.com/paper/1905.09971/) (2019)
- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [Scalable and Accurate Variational Bayes for High-Dimensional Binary Regression Models](https://mlsanity.com/paper/1911.06743/) (2019)
- [Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation](https://mlsanity.com/paper/1506.08640/) (2015)
- [Unbiased Markov chain Monte Carlo with couplings](https://mlsanity.com/paper/1708.03625/) (2017)
- [Partially factorized variational inference for high-dimensional mixed models](https://mlsanity.com/paper/2312.13148/) (2023)
- [Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results](https://mlsanity.com/paper/2206.08118/) (2022)
- [A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal One](https://mlsanity.com/paper/2007.06944/) (2020)
- [Ultimate P'olya Gamma Samplers -- Efficient MCMC for possibly imbalanced binary and categorical data](https://mlsanity.com/paper/2011.06898/) (2020)
- [Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regression](https://mlsanity.com/paper/2412.07999/) (2024)
- [Linear-cost unbiased posterior estimates for crossed effects and matrix factorization models via couplings](https://mlsanity.com/paper/2410.08939/) (2024)
- [Conjugate gradient methods for high-dimensional GLMMs](https://mlsanity.com/paper/2411.04729/) (2024)

## Built on by (most cited first, 2 of 2)

- [Wasserstein Contraction of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2605.30253/) (2026)
- [Spectral gap of Metropolis-within-Gibbs under log-concavity](https://mlsanity.com/paper/2509.26175/) (2025)

## Abstract (arXiv)

We investigate the convergence properties of popular data-augmentation samplers for Baye-sian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the associated mixing times (in Kullback-Leibler divergence). The bounds depend explicitly on the design matrix and the prior precision, while they hold uniformly over the vector of responses. We specialize the results for different regimes of statistical interest, when both the number of data points n and parameters p are large: in particular we identify scenarios where the mixing times remain bounded as n,p→∞, and ones where they do not. The results are shown to be tight (in the worst case with respect to the responses) and provide guidance on choices of prior distributions that provably lead to fast mixing. An empirical analysis based on coupling techniques suggests that the bounds are effective in predicting practically observed behaviours.