WNCG Seminar: Uncertainty quantification and active sampling for low-rank matrices

Friday, February 22, 2019
11:00am - 12:00pm
EER 1.516 (North Tower)

Abstract: We present a new statistical framework to quantify uncertainty (UQ) for recovering low-rank matrices from incomplete and noisy observations. We further develop a sequential active sampling approach guided by the uncertainties. The motivation comes from two related and widely studied problems, matrix completion, which aims to recover a low-rank matrix X from a partial, noisy observation of its entries, and low-rank matrix recovery, which recovers X from a set of linear combination its entries with additive noise. The proposed framework reveals several novel insights on the role of coherence metric and coding design (e.g., Latin squares and Kerdock codes) on the sampling performance and UQ for noisy matrix completion and recovery. Using such insights, we develop an efficient posterior sampler for UQ, which is then used to guide a closed-form sampling scheme for matrix entries. We showed the competitive performance of this integrated sampling / UQ methodology in simulation studies and two applications to collaborative filtering, compared with existing approaches. This is joint work with Simon Mak and Shaowu Yuchi at Georgia Tech.


Assistant Professor
Georgia Institute of Technology

Yao Xie is an Assistant Professor at Georgia Institute of Technology in the H. Milton Stewart School of Industrial and Systems Engineering. She received her Ph.D. in Electrical Engineering (minor in Mathematics) from Stanford University, M.Sc. in Electrical and Computer Engineering from the University of Florida, and B.Sc. in Electrical Engineering and Computer Science from University of Science and Technology of China (USTC). She was a Research Scientist at Duke University. Her research interests are statistical machine learning and signal processing, in providing the theoretical foundation as well as developing computationally efficient and statistically powerful algorithms. She has worked on such problems in sensor networks, social networks, power systems, crime data analysis,  and wireless communications. She received the National Science Foundation (NSF) CAREER Award in 2017.