This is one of a series of talks that are given by Professor Chen. The full list of his talks is as follows:
Wednesday, August 28, 2019; 11:00 am - 12:00 pm; Groseclose 402
Thursday, August 29, 2019; 11:00 am - 12:00 pm; Groseclose 402
Tuesday, September 3, 2019; 11:00 am - 12:00 pm; Main - Executive Education Room 228
Wednesday, September 4, 2019; 11:00 am - 12:00 pm; Main - Executive Education Room 228
Thursday, September 5, 2019; 11:00 am - 12:00 pm; Groseclose 402

Check https://triad.gatech.edu/events for more information. 
For location information, please check https://isye.gatech.edu/about/maps-directions/isye-building-complex

Title of this talk: Inference and Uncertainty Quantification for Noise Matrix Completion

Abstract: 

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g. constructing a valid and short confidence interval for an unseen entry).

This talk takes a step towards inference and uncertainty quantification for noisy matrix completion. We develop a simple procedure to compensate for the bias of the widely used convex and nonconvex estimators. The resulting de-biased estimators admit nearly precise non-asymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals/regions for, say, the missing entries and the low-rank factors. Our inferential procedures do not rely on sample splitting, thus avoiding unnecessary loss of data efficiency. As a byproduct, we obtain a sharp characterization of the estimation accuracy of our de-biased estimators, which, to the best of our knowledge, are the first tractable algorithms that provably achieve full statistical efficiency (including the preconstant). The analysis herein is built upon the intimate link between convex and nonconvex optimization.

This is joint work with Cong Ma, Yuling Yan, Yuejie Chi, 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.