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Inference and uncertainty quantification for noisy matrix completion.

Yuxin Chen1, Jianqing Fan2, Cong Ma2

  • 1Department of Electrical Engineering, Princeton University, Princeton, NJ 08544; yuxin.chen@princeton.edu.

Proceedings of the National Academy of Sciences of the United States of America
|November 1, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a debiased estimator for noisy matrix completion, enabling accurate uncertainty assessment and efficient statistical inference for low-rank matrices. This method provides optimal confidence intervals without sample splitting, achieving full statistical efficiency.

Keywords:
confidence intervalsconvex relaxationnonconvex optimization

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Noisy matrix completion estimates low-rank matrices from partial, corrupted data.
  • Assessing uncertainty and performing statistical inference remain challenging.

Purpose of the Study:

  • Develop a debiased estimator for noisy matrix completion.
  • Enable precise uncertainty quantification and statistical inference.

Main Methods:

  • A simple bias compensation procedure is developed.
  • Nonasymptotic distributional characterizations are derived for debiased estimators.
  • Optimal confidence intervals are constructed for missing entries and low-rank factors.

Main Results:

  • Debiased estimators achieve nearly precise nonasymptotic distributional characterizations.
  • Inferential procedures avoid sample splitting, enhancing data efficiency.
  • Sharp characterization of estimation accuracy (rate and constant) is obtained.

Conclusions:

  • The proposed debiased estimators are tractable and achieve full statistical efficiency.
  • This work provides a significant advancement in uncertainty assessment for noisy matrix completion.
  • Optimal confidence intervals can be constructed efficiently.