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A simple method for rejection sampling efficiency improvement on SIMT architectures

机译：一种简单的抑制SIMT架构采样效率改进方法

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摘要

We derive a probability distribution for the possible number of iterations required for a SIMT (single instruction multiple thread) program using rejection sampling to finish creating a sample across all threads. This distribution is found to match a recently proposed distribution from Chakraborty and Gupta (in: Communications in statistics: theory and methods, 2015) that was shown as a good approximation of certain datasets. This work demonstrates an exact application of this distribution. The distribution can be used to evaluate the relative merit of some sampling methods on the GPU without resort to numerical tests. The distribution reduces to the expected geometric distribution in the single thread per warp limit. A simplified formula to approximate the expected number of iterations required to obtain rejection iteration samples is provided. With this new result, a simple, efficient layout for assigning sampling tasks to threads on a GPU is found as a function of the rejection probability without recourse to more complicated rejection sampling methods.
机译：我们使用拒绝采样来实现SIMT（单指令多线程）程序所需的可能数量的概率分布，以完成所有线程的创建样本。发现该分布与Chakraborty和Gupta最近提出的分发相匹配（统计：统计中的通信：2015）所示的近似数据集的良好近似值。这项工作展示了这种分布的精确应用。该分布可用于评估GPU上一些采样方法的相对优点，而无需诉诸数值测试。该分布减少了每条曲线限制的单个线程中的预期几何分布。提供了一种近似获得获得抑制迭代样本所需的预期迭代次数的简化公式。通过这种新的结果，可以在没有求助于更复杂的抑制采样方法的拒绝概率的函数中发现用于将采样任务分配给GPU上线程的采样任务的简单高效布局。

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