梁鑫博士学术报告(12月8日)

时间:2018-12-06   浏览:134

报告题目: 

Convergence Analysis of the Oja-Karhunen Algorithm for Principal Component Analysis


报告人: 梁鑫 博士

报告人单位:清华大学

报告时间:2018年12月8日,下午14:00-15:30

报告地点:数学学院第一报告厅 


报告摘要:

   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, DOI 10.1007/s10107-017-1182-z], 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.


报告人介绍:

梁鑫,2014年于北京大学数学科学学院获得理学博士学位。其后分别在马克斯普朗克复杂技术系统动力学研究所、新竹交通大学从事博士后研究。2018年起于清华大学丘成桐数学科学中心任助理教授,从事矩阵理论和数值线性代数方向的研究,重点关注特征值问题的理论分析及其在偏微分方程、数据科学中的应用。