English(EN) Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run

新分析改进了Hit-and-Run马尔可夫链的谱隙

作者 PulseAugur 编辑部 · [1 个来源] · 2026-08-18 04:00

研究人员分析了凸体上Hit-and-Run和Coordinate Hit-and-Run马尔可夫链的谱隙。该研究改进了Hit-and-Run的现有收敛界限，将维度依赖性从三次改进到近二次。这项工作将Hit-and-Run的收敛性与Poincaré和KLS常数联系起来，这是一种先前用于Ball walk的技术。该分析还引入了一种使用对偶和微积分的新方法，从而改进了Coordinate Hit-and-Run的混合时间。 AI

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arXiv cs.LG TIER_1 English(EN) · Yunbum Kook, Santosh S. Vempala · 2026-08-18 04:00

Hit-and-Run 和 Coordinate Hit-and-Run 的谱隙

arXiv:2608.16878v1 Announce Type: cross Abstract: For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $\Omega(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincar\'e constant of the uniform distribution $\…

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Hit-and-Run 和 Coordinate Hit-and-Run 的谱隙

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