Inference and uncertainty quantification for noisy matrix completion

• DOI: 10.1073/pnas.1910053116
• Publication Date: 2019-10-30T23:24:16Z
• Authors: Yuxin Chen; Jianqing Fan; Cong Ma; Yuling Yan
• Keywords: Matrix Completion; Rank (graph theory); Statistical Inference; Matrix (chemical analysis)

Significance Matrix completion finds numerous applications in data science, ranging from information retrieval to medical imaging. While substantial progress has been made designing estimation algorithms, it remains unknown how perform optimal statistical inference on the matrix given obtained estimates—a task at core of modern decision making. We propose procedures debias popular convex and nonconvex estimators derive distributional characterizations for resulting debiased estimators. This theory enables valid matrix. Our 1) yield construction confidence intervals missing entries 2) achieve accuracy a sharp manner.