An iterative penalized least squares approach to sparse canonical correlation analysis
An iterative penalized least squares approach to sparse canonical correlation analysis
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DOI：
10.1111/biom.13043
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发表时间：
2019-09-01
期刊：
影响因子：
1.9
通讯作者：
Zhang, Xin
中科院分区：
文献类型：
--
作者：
Mai, Qing;Zhang, Xin
对具有潜在高相关性的两组高维测量之间的关系进行建模越来越有趣。典型相关分析（CCA）是研究两个多元随机变量之间的依赖关系并提取高度相关线性组合的典型对的经典工具。在基因组学、文本挖掘和成像研究等领域的应用推动下，最近的许多研究将CCA推广到高维环境。然而，他们中的大多数要么依赖于强假设的协方差矩阵，或不产生嵌套的解决方案。我们提出了一种新的稀疏CCA（SCCA）方法，重铸高维CCA作为一个迭代惩罚最小二乘问题。由于新的迭代惩罚最小二乘公式，我们的方法直接估计稀疏CCA方向与有效的算法。因此，与现有的一些方法相比，新的SCCA不对协方差矩阵施加任何稀疏性假设。建议的SCCA也是非常灵活的意义上，它可以很容易地结合适当选择的惩罚函数来执行结构化变量选择，并纳入先验信息。此外，我们的建议SCCA产生嵌套的解决方案，从而提供了很大的方便，在实践中。理论结果表明，SCCA可以一致地估计真正的典型对在超高的维度，以压倒性的概率。数值结果也证明了SCCA的竞争力。
It is increasingly interesting to model the relationship between two sets of high-dimensional measurements with potentially high correlations. Canonical correlation analysis (CCA) is a classical tool that explores the dependency of two multivariate random variables and extracts canonical pairs of highly correlated linear combinations. Driven by applications in genomics, text mining, and imaging research, among others, many recent studies generalize CCA to high-dimensional settings. However, most of them either rely on strong assumptions on covariance matrices, or do not produce nested solutions. We propose a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. Thanks to the new iterative penalized least squares formulation, our method directly estimates the sparse CCA directions with efficient algorithms. Therefore, in contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices. The proposed SCCA is also very flexible in the sense that it can be easily combined with properly chosen penalty functions to perform structured variable selection and incorporate prior information. Moreover, our proposal of SCCA produces nested solutions and thus provides great convenient in practice. Theoretical results show that SCCA can consistently estimate the true canonical pairs with an overwhelming probability in ultra-high dimensions. Numerical results also demonstrate the competitive performance of SCCA.