Bibliographic Information: Gaitonde, J., & Mossel, E. (2024). Comparison Theorems for the Mixing Times of Systematic and Random Scan Dynamics. arXiv preprint arXiv:2410.11136.
Research Objective: This paper investigates the relationship between the mixing times of two common Gibbs sampling methods: systematic scan and random scan (Glauber dynamics). The authors aim to establish tight bounds comparing the efficiency of these methods for sampling from high-dimensional distributions.
Methodology: The authors employ linear-algebraic techniques to analyze the operator norms of transition matrices associated with systematic and random scan Gibbs samplers. They leverage the properties of orthogonal projections and spectral gap analysis to derive their results.
Key Findings:
Main Conclusions: The paper provides a comprehensive understanding of the relative performance between systematic and random scan Gibbs samplers. The tight bounds derived in the paper offer theoretical guarantees for the efficiency of systematic scan sampling, which is often preferred in practice due to its computational advantages.
Significance: This work contributes significantly to the field of Markov chain Monte Carlo (MCMC) methods, particularly in the context of high-dimensional sampling. The results have implications for various applications, including statistics, computer science, and machine learning, where efficient sampling from complex distributions is crucial.
Limitations and Future Research: While the paper establishes tight bounds for the worst-case scenario, further research could explore scenarios where the systematic scan might outperform Glauber dynamics. Additionally, investigating the impact of specific scan orders on mixing times could provide valuable insights for practical implementations.
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by Jason Gaiton... at arxiv.org 10-16-2024
https://arxiv.org/pdf/2410.11136.pdfDeeper Inquiries