An ADMM with continuation algorithm for non-convex SICA-penalized regression in high dimensions
An ADMM with continuation algorithm for non-convex SICA-penalized regression in high dimensions
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DOI：
10.1080/00949655.2018.1448397
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发表时间：
2018-03
影响因子：
1.2
通讯作者：
Yueyong Shi;Yuanshan Wu;Deyi Xu;Yuling Jiao
中科院分区：
文献类型：
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作者：
Yueyong Shi;Yuanshan Wu;Deyi Xu;Yuling Jiao
摘要 计数与绝对偏差平滑积分（SICA）惩罚已在理论和实践中被证明在变量选择的非凸惩罚中是有效的。然而，由于原点的奇异性和 SICA 罚函数的非凸性，当变量数量超过样本量时，解决与 SICA 罚函数相关的非凸优化问题仍有待丰富。在本文中，我们开发了一种高效、准确的乘法器交替方向方法和连续算法，用于解决高维中的 SICA 惩罚最小二乘问题。我们在一些温和的规律性条件下建立了该算法的收敛性，并研究了相应的Karush-Kuhn-Tucker最优性条件。开发了高维贝叶斯信息准则来选择最佳调整参数。我们进行了广泛的模拟研究来评估所提出算法的效率和准确性，同时通过高维微阵列研究进一步说明了其实际用途。
Abstract The smooth integration of counting and absolute deviation (SICA) penalty has been demonstrated theoretically and practically to be effective in non-convex penalization for variable selection. However, solving the non-convex optimization problem associated with the SICA penalty when the number of variables exceeds the sample size remains to be enriched due to the singularity at the origin and the non-convexity of the SICA penalty function. In this paper, we develop an efficient and accurate alternating direction method of multipliers with continuation algorithm for solving the SICA-penalized least squares problem in high dimensions. We establish the convergence property of the proposed algorithm under some mild regularity conditions and study the corresponding Karush–Kuhn–Tucker optimality condition. A high-dimensional Bayesian information criterion is developed to select the optimal tuning parameters. We conduct extensive simulations studies to evaluate the efficiency and accuracy of the proposed algorithm, while its practical usefulness is further illustrated with a high-dimensional microarray study.