Sequential low-rank matrix completion and estimation: Uncertainty quantification and design

Series: 
Stochastics Seminar
Thursday, October 19, 2017 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
ISyE, Georgia Institute of Technology
Organizer: 
We present a unified framework for sequential low-rank matrix completion and estimation, address the joint goals of uncertainty quantification (UQ) and statistical design. The first goal of UQ aims to provide a measure of uncertainty of estimated entries in the unknown low-rank matrix X, while the second goal of statistical design provides an informed sampling or measurement scheme for observing the entries in X. For UQ, we adopt a Bayesian approach and assume a singular matrix-variate Gaussian prior the low-rank matrix X which enjoys conjugacy. For design, we explore deterministic design from information-theoretic coding theory. The effectiveness of our proposed methodology is then illustrated on applications to collaborative filtering.