Inference and uncertainty quantification for noisy matrix completion

Yuxin Chen, Jianqing Fan, Cong Ma, Yuling Yan

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite remarkable progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform efficient statistical inference on the unknown matrix (e.g., constructing a valid and short confidence interval for an unseen entry). This paper takes a substantial step toward addressing such tasks. We develop a simple procedure to compensate for the bias of the widely used convex and nonconvex estimators. The resulting debiased estimators admit nearly precise nonasymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals/regions for, say, the missing entries and the low-rank factors. Our inferential procedures do not require sample splitting, thus avoiding unnecessary loss of data efficiency. As a byproduct, we obtain a sharp characterization of the estimation accuracy of our debiased estimators in both rate and constant. Our debiased estimators are tractable algorithms that provably achieve full statistical efficiency.

Original languageEnglish (US)
Pages (from-to)22931-22937
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number46
StatePublished - Nov 12 2019

All Science Journal Classification (ASJC) codes

  • General


  • Confidence intervals
  • Convex relaxation
  • Nonconvex optimization


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