Hit-and-Run蒙特卡洛中的弹道收敛与一种无坐标随机Kaczmarz算法
Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithm
AI总结：
本文通过耦合方法证明高斯目标下Hit-and-Run的Wasserstein收缩尖锐估计，揭示弹道与超扩散收敛，并推广至无坐标随机Kaczmarz算法，为无坐标采样与优化提供新见解。
摘要：
Hit-and-Run是一种无坐标的Gibbs采样器，然而其无坐标性质的定量优势在很大程度上仍未被探索，仅停留在实证研究层面。在本文中，我们通过耦合方法证明了高斯目标测度下Hit-and-Run的Wasserstein收缩的尖锐估计，并得出了混合时间界。我们的结果揭示了在某些设定下的弹道和超扩散收敛速率。此外，我们将这些见解扩展到随机Kaczmarz算法（一种用于线性系统的迭代方法）的无坐标变体，并证明了类似的收敛速率。这些发现为无坐标方法在采样和优化中的优势与局限性提供了新的见解。
英文摘要：
Hit-and-Run is a coordinate-free Gibbs sampler, yet the quantitative advantages of its coordinate-free property remain largely unexplored beyond empirical studies. In this paper, we prove sharp estimates for the Wasserstein contraction of Hit-and-Run in Gaussian target measures via coupling methods and conclude mixing time bounds. Our results uncover ballistic and superdiffusive convergence rates in certain settings. Furthermore, we extend these insights to a coordinate-free variant of the randomized Kaczmarz algorithm, an iterative method for linear systems, and demonstrate analogous convergence rates. These findings offer new insights into the advantages and limitations of coordinate-free methods for both sampling and optimization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
