Singular Value Decomposition for High-Dimensional Data
主 题: Singular Value Decomposition for High-Dimensional Data
报告人: Dan Yang (Rutgers University)
时 间: 2014-07-03 14:00-15:00
地 点: 理科一号楼1479教室（统计中心活动）
Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. In this talk, we suppose the true singular vectors have sparse representations in a certain basis. We propose an iterative thresholding algorithm that can estimate the subspaces spanned by leading left and right singular vectors and also the true mean matrix optimally under Gaussian assumption. We further turn the algorithm into a practical methodology that is fast, data-driven and robust to heavy-tailed noises. Simulations and a real data example further show its competitive performance.
About the speaker（报告人介绍）：I got my bachelor degree in both Statistics and Economics from Peking University in 2007 and Ph.D. degree in Statistics from University of Pennsylvania under the supervision of Professors Andreas Buja and Zongming Ma in 2012. I spent a year at Statistical and Applied Mathematical Sciences Institute as a postdoc from 2012 to 2013. I am now an assistant professor at Rutgers University.