Accelerating Large-Scale Statistical Computation With the GOEM Algorithm
Accelerating Large-Scale Statistical Computation With the GOEM Algorithm
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DOI：
10.1080/00401706.2016.1256840
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发表时间：
2017-05
期刊：
影响因子：
2.5
通讯作者：
Xiao Nie;J. Huling;Peter Z. G. Qian
中科院分区：
文献类型：
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作者：
Xiao Nie;J. Huling;Peter Z. G. Qian
**摘要** 大规模数据分析问题在许多学科中变得越来越普遍。虽然大量的数据提供了更强的统计能力，但它也带来了计算方面的挑战。熊等人提出的正交化期望最大化（EM）算法从设计的角度来看是一种处理大规模最小二乘问题的有效方法。在本文中，我们对正交化EM算法进行了重新表述和推广。确定了计算复杂度和收敛性保证。正交化EM算法的重新表述降低了最小二乘问题和惩罚最小二乘问题的计算复杂度。这种重新表述被称为GOEM（广义正交化EM）算法，它可以包含各种各样的凸惩罚和非凸惩罚，包括套索惩罚、组套索惩罚和极小极大凹惩罚。GOEM算法进一步扩展到更广泛的模型类别，包括广义线性模型和考克斯比例风险模型。文中包含了合成数据和实际数据的例子，以说明与标准技术相比它的使用方法和效率。本文的补充材料可在线获取。
ABSTRACT Large-scale data analysis problems have become increasingly common across many disciplines. While large volume of data offers more statistical power, it also brings computational challenges. The orthogonalizing expectation–maximization (EM) algorithm by Xiong et al. is an efficient method to deal with large-scale least-square problems from a design point of view. In this article, we propose a reformulation and generalization of the orthogonalizing EM algorithm. Computational complexity and convergence guarantees are established. The reformulation of the orthogonalizing EM algorithm leads to a reduction in computational complexity for least-square problems and penalized least-square problems. The reformulation, named the GOEM (generalized orthogonalizing EM) algorithm, can incorporate a wide variety of convex and nonconvex penalties, including the lasso, group lasso, and minimax concave penalty penalties. The GOEM algorithm is further extended to a wider class of models including generalized linear models and Cox's proportional hazards model. Synthetic and real data examples are included to illustrate its use and efficiency compared with standard techniques. Supplementary materials for this article are available online.