A1232
Title: Optimal regularization of the first principal component
Authors: Youhong Lee - University of California, Santa Barbara (United States) [presenting]
Abstract: The concept of regularization, which combines a simple structured target with traditional estimators, is widely used in high-dimensional data analysis. A novel regularization technique and its efficient machine learning algorithm, termed direction-regularized principal component analysis (drPCA), are introduced. This method addresses the PCA problem, aiming to identify the direction of maximum variance in the data while adhering to a predefined target direction. Using the high-dimensional, low-sample size framework, an asymptotic analysis of the solution is performed, which results in an optimal tuning parameter that minimizes an asymptotic loss function. The data rapidly acquires the estimator corresponding to the optimal tuning parameter. Furthermore, it is demonstrated that under certain covariance structures, the estimator is equivalent to both the Ledoit-Wolf constant correlation shrinkage estimator and a recently proposed James-Stein estimator for the first principal component.
