Estimating High-dimensional Matrices: Convex Geometry and Computational Barriers
主 题: Estimating High-dimensional Matrices: Convex Geometry and Computational Barriers
报告人: Dr. Zongming Ma (University of Pennsylvania)
时 间: 2013-11-05 14:00
地 点: 理科一号楼1303（统计中心活动）
Statistical inference of large matrices arises frequently in the analysis of massive datasets. In this talk, I introduce a new machinery for studying estimation of high-dimensional matrices, which yields tight non-asymptotic minimax rates for a large collection of loss functions in a variety of problems. Based on the convex geometry of finite-dimensional Banach spaces, the minimax rates of oracle (unconstrained) Gaussian denoising problem is determined for all unitarily invariant norms. This result is then extended to denoising with submatrix sparsity, where the excess risk depends on the sparsity constraints in a completely different manner. Moreover, the approach is applicable to the matrix completion under the low-rank constraint and extends far beyond the normal mean model. In the final part of the talk, I will give an example where attaining the minimax rate is provably hard in a complexity-theoretic sense. This observation reveals that there can exist a significant gap between the statistical fundamental limit and what can be achieved by computationally efficient procedures. This talk is based on joint work with Yihong Wu (UIUC).
Short Bio of Dr. Ma:
Zongming Ma received his B.S. in Mathematics from Peking University, China, in 2005 and Ph.D. in Statistics from Stanford University in 2010. He has been an assistant professor in the Department of Statistics of The Wharton School, University of Pennsylvania since 2010. His research interests include high-dimensional statistical inference and nonparametric statistics.
