完美的空间混合采样

Pub Date : 2022-12-01 Epub Date: 2022-02-18 DOI:10.1002/rsa.21079

Weiming Feng, Heng Guo, Yitong Yin

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引用次数: 0

摘要

我们引入了一种新的完美采样技术，它可以应用于一般的吉布斯分布，而且如果相关性的衰减速度快于邻域增长速度，运行时间也是线性的。特别是在ℤ d 这样具有亚指数邻域增长的图中，只要吉布斯采样快速混合，我们的算法就能实现线性运行时间。在具体应用中，我们得到了目前在这类图中用于着色和单体-二聚体模型的最佳完美采样器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Perfect sampling from spatial mixing.

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like $ℤ^{d}$ , our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.

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