论文标题
有效的半平滑牛顿增强拉格朗日弹性网的方法
An Efficient Semi-smooth Newton Augmented Lagrangian Method for Elastic Net
论文作者
论文摘要
特征选择是统计和机器学习中重要而活跃的研究领域。弹性网通常用于执行选择时，当特征表现出不可忽略的共线性或从业者希望结合其他已知结构。在本文中，我们提出了一种新的半光滑牛顿增强拉格朗日方法，以在超高维度中有效地解决弹性网。我们的新算法利用了由于增强拉格朗日的第二阶信息而引起的弹性净罚球引起的稀疏性和稀疏性。这大大降低了问题的计算成本。在合成数据集和真实数据集上使用模拟，我们证明我们的方法在CPU时间上至少要超过其最佳竞争对手。我们还将我们的方法应用于有关儿童肥胖症的基因组广泛关联研究。
Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate additional known structure. In this article, we propose a new Semi-smooth Newton Augmented Lagrangian Method to efficiently solve the Elastic Net in ultra-high dimensional settings. Our new algorithm exploits both the sparsity induced by the Elastic Net penalty and the sparsity due to the second order information of the augmented Lagrangian. This greatly reduces the computational cost of the problem. Using simulations on both synthetic and real datasets, we demonstrate that our approach outperforms its best competitors by at least an order of magnitude in terms of CPU time. We also apply our approach to a Genome Wide Association Study on childhood obesity.
