English(EN) Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

新的马尔可夫链蒙特卡洛方法提高了重尾分布的采样效率

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-26 04:00

研究人员开发了一种新的 महत्त्व退火马尔可夫链蒙特卡洛（MCMC）采样方法，专门用于具有重尾的目标。该研究证明，在与目标分布的尾部衰减率和退火参数 beta 相关的某些条件下，这种连续时间链是均匀遍历的。此外，链的谱隙是可以控制的，并且模拟表明，与标准的 RWM 相比，适当的退火可以显著提高效率并降低对初始化的敏感性。 AI

影响通过改进复杂数据分布的马尔可夫链蒙特卡洛采样技术，这项研究可能带来更高效的 AI 模型训练和分析。

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arXiv stat.ML TIER_1 English(EN) · Quan Zhou · 2026-10-26 04:00

Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

arXiv:2506.19186v2 Announce Type: replace-cross Abstract: We study the importance-tempered random-walk Metropolis (RWM) algorithm on $\mathbb{R}^d$, which targets the tempered density $\pi_\beta(x) \propto \pi(x)^\beta$ with $\beta \in (0,1)$ and corrects for the resulting bias b…

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Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

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