mlsanityData to 14 Oct 2026

Spectral gap of Metropolis-within-Gibbs under log-concavity

arXiv 2509.26175 ↗First posted 30 Sep 2025stat.ML math.ST stat.MEcited by 0

Not on the map. Why?

Abstract (arXiv)

The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov chain Monte Carlo method for sampling from high-dimensional distributions when exact conditional sampling is intractable. We study MwG with Random Walk Metropolis (RWM) updates, whose proposal variances are uniformly comparable to the corresponding conditional variances. Assuming the target π is a d-dimensional log-concave distribution with condition number kappa, we establish a spectral gap lower bound of order Omega((kappa d)-1) for the random-scan version of MwG, improving on the previously available Omega((kappa2 d)-1) bound. This is obtained by developing sharp estimates of the conductance of one-dimensional RWM kernels, which may be of independent interest. The result shows that MwG can mix substantially faster under the stated uniform tuning condition and that its mixing performance is just a constant factor worse than that of the exact Gibbs sampler, thus providing theoretical support to previously observed empirical behavior.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 13 of its 36 references that are in the map. First posted on arXiv 30 Sep 2025.

Builds on

13 of 36 references.

References · 13

  1. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 118
  2. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  3. 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 13
  4. 2019MALA-within-Gibbs samplers for high-dimensional distributions with sparse conditional structurecited by 8
  5. 2020Random Coordinate Langevin Monte Carlocited by 7
  6. 2020Random Coordinate Underdamped Langevin Monte Carlocited by 6
  7. 2022Clustering consistency with Dirichlet process mixturescited by 6
  8. 2024Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian modelscited by 4
  9. 2024Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regressioncited by 3
  10. 2022Spectral Telescope: Convergence Rate Bounds for Random-Scan Gibbs Samplers Based on a Hierarchical Structurecited by 2
  11. 2024Is Gibbs sampling faster than Hamiltonian Monte Carlo on GLMs?cited by 2
  12. 2025Mixing times of data-augmentation Gibbs samplers for high-dimensional probit regressioncited by 2
1 more
  1. 2014A practical sequential stopping rule for high-dimensional MCMC and its application to spatial-temporal Bayesian modelscited by 1

Built on by

Not cited yet.