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Title of this talk: Spectral Methods Meets Asymmetry:  Two Recent Stories

Abstract: This talk is concerned with the interplay between asymmetry and spectral methods. Imagine that we have access to an asymmetrically perturbed low-rank data matrix. We attempt estimation of the low-rank matrix via eigen-decomposition --- an uncommon approach when dealing with non-symmetric matrices.

We provide two recent stories to demonstrate the advantages and effectiveness of this approach.   The first story is concerned with top-K ranking from pairwise comparisons,  for which the spectral method enables un-improvable ranking accuracy.  The second story is concerned with matrix de-noising and spectral estimation, for which the eigen-decomposition method significantly outperforms the (unadjusted) SVD-based approach and is fully adaptive to heteroscedasticity without the need of careful bias correction.

The first part of this talk is based on joint work with Cong Ma, Kaizheng Wang, and Jianqing Fan;  the second part of this talk is based on joint work with Chen Cheng and Jianqing Fan.
 

Bio: Yuxin Chen is currently an assistant professor in the Department of Electrical Engineering at Princeton University. Prior to joining Princeton, he was a postdoctoral scholar in the Department of Statistics at Stanford University, and he completed his Ph.D. in Electrical Engineering at Stanford University. His research interests include high-dimensional statistics, convex and nonconvex optimization, statistical learning, and information theory. He received the 2019 AFOSR Young Investigator Award.