Gradient-based Sparse Principal Component Analysis with Extensions to Online Learning
Gradient-based Sparse Principal Component Analysis with Extensions to Online Learning
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DOI：
10.1093/biomet/asac041
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发表时间：
2019-11
期刊：
影响因子：
2.7
通讯作者：
Yixuan Qiu;Jing Lei;K. Roeder
中科院分区：
文献类型：
--
作者：
Yixuan Qiu;Jing Lei;K. Roeder
稀疏主成分分析是高维数据同时降维和变量选择的重要技术。在这项工作中，我们将稀疏主成分分析问题的独特几何结构与凸优化的最新进展相结合，开发了一种新的基于梯度的稀疏主成分分析算法。这些算法与原始的乘法器交替方向方法具有相同的全局收敛性保证，并且可以使用深度学习文献中为梯度方法开发的丰富工具箱更有效地实现。最值得注意的是，这些基于梯度的算法可以与随机梯度下降方法相结合，产生有效的在线稀疏主成分分析算法，具有可证明的数值和统计性能保证。各种仿真研究证明了新算法的实际性能和实用性。作为一个应用，我们展示了我们的方法的可扩展性和统计准确性如何使我们能够在高维RNA测序数据中找到有趣的功能基因群。
Sparse principal component analysis is an important technique for simultaneous dimensionality reduction and variable selection with high-dimensional data. In this work we combine the unique geometric structure of the sparse principal component analysis problem with recent advances in convex optimization to develop novel gradient-based sparse principal component analysis algorithms. These algorithms enjoy the same global convergence guarantee as the original alternating direction method of multipliers, and can be more efficiently implemented with the rich toolbox developed for gradient methods from the deep learning literature. Most notably, these gradient-based algorithms can be combined with stochastic gradient descent methods to produce efficient online sparse principal component analysis algorithms with provable numerical and statistical performance guarantees. The practical performance and usefulness of the new algorithms are demonstrated in various simulation studies. As an application, we show how the scalability and statistical accuracy of our method enable us to find interesting functional gene groups in high-dimensional RNA sequencing data.