This week's Statistics Seminar Speaker will be Haipeng Shen from UNC Chapel Hill.
Talk Title: Principal Component Analysis: Regularization and Asymptotics
Principal component analysis (PCA) is a ubiquitous technique for dimension reduction of multivariate data. Regularization of PCA becomes essential for high dimensionality. Maximizing variance of a standardized linear combination of variables is the standard textbook treatment of PCA. A more general perspective of PCA is by way of fitting low rank approximations to the data matrix. I shall take this low-rank-approximation perspective and describe a general regularization framework for PCA, that leads to alternative approaches for functional PCA and sparse PCA. I shall then introduce a general asymptotic framework for studying consistency properties of PCA and its regularized siblings. The framework includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains.
Refreshments will be served after the seminar in 1181 Comstock Hall.