Sampling With Replacement vs Poisson Sampling: A Comparative Study in Optimal Subsampling
Sampling With Replacement vs Poisson Sampling: A Comparative Study in Optimal Subsampling
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DOI：
10.1109/tit.2022.3176955
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发表时间：
2022-05
影响因子：
2.5
通讯作者：
Jing Wang;Jiahui Zou;HaiYing Wang
中科院分区：
文献类型：
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作者：
Jing Wang;Jiahui Zou;HaiYing Wang
面对海量数据，子抽样是一种常用的提高计算效率的技术，而使用非均匀子抽样概率是提高估计效率的有效途径。为了提高计算效率，子采样通常采用替换或泊松子采样来实现。然而，对于这两种子抽样方法在估计效率和计算便利性等方面的差异，目前还没有进行严格的研究。本文对这两种不同的抽样方法进行了比较研究。在一般目标函数极大化的背景下，我们首先推导了由两个抽样过程得到的估计量的渐近分布。结果表明，泊松子抽样具有较高的估计效率。基于置换子抽样和泊松子抽样的渐近分布，导出了使子抽样估计量方差函数最小的最优子抽样概率。这些子抽样概率进一步揭示了置换子抽样与泊松子抽样的异同。通过对两种子抽样方法的理论描述和比较，为在实践中选择更合适的子抽样方法提供了指导。在此基础上，提出了切实可行的算法，并通过理论分析和实证分析对算法进行了评价。
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency, subsampling is often implemented with replacement or through Poisson subsampling. However, no rigorous investigation has been performed to study the difference between the two subsampling procedures such as their estimation efficiency and computational convenience. This paper performs a comparative study on these two different sampling procedures. In the context of maximizing a general target function, we first derive asymptotic distributions for estimators obtained from the two sampling procedures. The results show that the Poisson subsampling may have a higher estimation efficiency. Based on the asymptotic distributions for both subsampling with replacement and Poisson subsampling, we derive optimal subsampling probabilities that minimize the variance functions of the subsampling estimators. These subsampling probabilities further reveal the similarities and differences between subsampling with replacement and Poisson subsampling. The theoretical characterizations and comparisons on the two subsampling procedures provide guidance to select a more appropriate subsampling approach in practice. Furthermore, practically implementable algorithms are proposed based on the optimal structural results, which are evaluated through both theoretical and empirical analyses.