Inference and uncertainty quantification for noisy matrix completion
Abstract
Matrix completion finds numerous applications in data science, ranging from information retrieval to medical imaging. While substantial progress has been made in designing estimation algorithms, it remains unknown how to perform optimal statistical inference on the unknown matrix given the obtained estimates—a task at the core of modern decision making. We propose procedures to debias the popular convex and nonconvex estimators and derive distributional characterizations for the resulting debiased estimators. This distributional theory enables valid inference on the unknown matrix. Our procedures 1) yield optimal construction of confidence intervals for missing entries and 2) achieve optimal estimation accuracy in a sharp manner.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 30, 2019
- Source ID
- 10.1073/pnas.1910053116
Entities
People
- Cong Ma
- Jianqing Fan
- Yuling Yan
- Yuxin Chen
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- National Institutes of Health
- National Science Foundation
- Office of Naval Research
- Princeton University