New spectral gap bound for Metropolis-within-Gibbs algorithm

Researchers have established a new spectral gap lower bound for the Metropolis-within-Gibbs (MwG) algorithm, a common Markov chain Monte Carlo method used for sampling from complex distributions. The study, focusing on MwG with Random Walk Metropolis updates under log-concavity assumptions, improved the existing bound from \(\\Omega((\\kappa^2 d)^{-1})\) to \(\\Omega((\\kappa d)^{-1})\). This theoretical advancement suggests that MwG can achieve significantly faster mixing rates when properly tuned, performing nearly as well as exact Gibbs samplers. AI

IMPACT Provides theoretical support for faster sampling in machine learning models, potentially improving training efficiency.

RANK_REASON Academic paper published on arXiv detailing theoretical advancements in MCMC algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• Cecilia Secchi
• Markov chain Monte Carlo
• Metropolis-within-Gibbs
• Random Walk Metropolis

• paper
• other

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