Information-Based Optimal Subdata Selection for Big Data Linear Regression
Information-Based Optimal Subdata Selection for Big Data Linear Regression
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DOI：
10.1080/01621459.2017.1408468
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发表时间：
2019-01-02
影响因子：
3.7
通讯作者：
Stufken, John
中科院分区：
文献类型：
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作者：
Wang, HaiYing;Yang, Min;Stufken, John
在许多科学分支中产生了大量的数据。由于计算的限制，已证实的统计方法不再适用于超大数据集。大数据分析的关键步骤是数据简化。现有的线性回归研究主要集中在基于次抽样的方法上。然而，这种方法不仅容易产生抽样误差，而且还会导致估计量的协方差矩阵，该矩阵通常由子数据大小的倒数数量级的项从下起限定。我们提出了一种新的方法，称为基于信息的最优子数据选择（IBOSS）。与现有的主要子数据方法相比，IBOSS方法具有以下优点：(1)速度明显快；（ii）适合分布式并行计算；（iii）即使子数据大小固定，随着全数据大小的增加，斜率参数估计量的方差收敛于0，即收敛速率取决于全数据大小；（iv） IBOSS子数据的数据分析简单明了，IBOSS估计器的抽样分布易于评估。理论结果和广泛的模拟表明，IBOSS方法优于基于子抽样的方法，有时优于几个数量级。通过对实际数据的分析，说明了新方法的优越性。本文的补充材料可在网上获得。
Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large datasets due to computational limitations. A critical step in big data analysis is data reduction. Existing investigations in the context of linear regression focus on subsampling-based methods. However, not only is this approach prone to sampling errors, it also leads to a covariance matrix of the estimators that is typically bounded from below by a term that is of the order of the inverse of the subdata size. We propose a novel approach, termed information-based optimal subdata selection (IBOSS). Compared to leading existing subdata methods, the IBOSS approach has the following advantages: (i) it is significantly faster; (ii) it is suitable for distributed parallel computing; (iii) the variances of the slope parameter estimators converge to 0 as the full data size increases even if the subdata size is fixed, that is, the convergence rate depends on the full data size; (iv) data analysis for IBOSS subdata is straightforward and the sampling distribution of an IBOSS estimator is easy to assess. Theoretical results and extensive simulations demonstrate that the IBOSS approach is superior to subsampling-based methods, sometimes by orders of magnitude. The advantages of the new approach are also illustrated through analysis of real data. Supplementary materials for this article are available online.