20190615 梁鑫 Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation

Title：Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation

报告人：梁鑫（清华大学）

时间：2019.06.15上午9:50-10:30

地点：数学院203报告厅

Abstract: Processing streaming data as they arrive is often necessary for high dimensional data analysis. In this talk, we analyze the convergence of a subspace online PCA iteration. Under the sub-Gaussian assumption, we obtain the finite-sample error bound that closely matches the minimax information lower bound by Vu and Lei [Ann. Statist. 41:6(2013), 2905-2947]. The case for the most significant principal component only, was solved by Li, Wang, Liu, and Zhang [Math. Program., Ser. B, 167:1(2018), 75-97], but a straightforward extension of their proofs, however, does not seem to work for the subspace case. People may see matrix analysis plays an important role in generalizing results for one-dimensional case to those for multi-dimensional case.