论文标题
一种不精确的歧管增强拉格朗日方法，用于自适应稀疏规范相关分析，并通过痕量套索正则化
An Inexact Manifold Augmented Lagrangian Method for Adaptive Sparse Canonical Correlation Analysis with Trace Lasso Regularization
论文作者
论文摘要
规范相关分析（简称CCA）通过找到最大化相关系数的这些变量的一些线性组合来描述两组变量之间的关系。但是，在变量数量超过样本量的高维设置中，或者在变量高度相关的情况下，传统的CCA不再适合。在本文中，通过使用Trace Lasso正则化提出了一种自适应稀疏版本的CCA（ASCCA）。当协变量高度相关时，提出的ASCCA减少了估计量的不稳定性，从而改善了其解释。 ASCCA进一步重新重新重新重新制定，以在Riemannian歧管上的优化问题，然后提出了一种不精确的Lagrangian方法，以解决由此产生的优化问题。将ASCCA的性能与不同模拟设置中的其他稀疏CCA技术进行了比较，这说明了ASCCA是可行和有效的。
Canonical correlation analysis (CCA for short) describes the relationship between two sets of variables by finding some linear combinations of these variables that maximizing the correlation coefficient. However, in high-dimensional settings where the number of variables exceeds sample size, or in the case of that the variables are highly correlated, the traditional CCA is no longer appropriate. In this paper, an adaptive sparse version of CCA (ASCCA for short) is proposed by using the trace Lasso regularization. The proposed ASCCA reduces the instability of the estimator when the covariates are highly correlated, and thus improves its interpretation. The ASCCA is further reformulated to an optimization problem on Riemannian manifolds, and an manifold inexact augmented Lagrangian method is then proposed for the resulting optimization problem. The performance of the ASCCA is compared with the other sparse CCA techniques in different simulation settings, which illustrates that the ASCCA is feasible and efficient.
