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

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.