mlsanityData to 7 Oct 2026

Inference and Uncertainty Quantification for Noisy Matrix Completion

arXiv 1906.04159 ↗First posted 10 Jun 2019stat.ML cs.IT cs.LGcited by 39

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Abstract (arXiv)

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g.~constructing a valid and short confidence interval for an unseen entry). This paper takes a step towards inference and uncertainty quantification for noisy matrix completion. We develop a simple procedure to compensate for the bias of the widely used convex and nonconvex estimators. The resulting de-biased estimators admit nearly precise non-asymptotic 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 rely on sample splitting, thus avoiding unnecessary loss of data efficiency. As a byproduct, we obtain a sharp characterization of the estimation accuracy of our de-biased estimators, which, to the best of our knowledge, are the first tractable algorithms that provably achieve full statistical efficiency (including the preconstant). The analysis herein is built upon the intimate link between convex and nonconvex optimization --- an appealing feature recently discovered by citechen2019noisy.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jun 2019.

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Citing papers per year: 2021: 12; 2022: 11; 2023: 5; 2024: 8; 2025: 1; 2026: 2.

39 papers.

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  1. 2021Causal Matrix Completioncited by 45
  2. 2021Uncertainty quantification in the Bradley-Terry-Luce modelcited by 28
  3. 2021Online Bootstrap Inference For Policy Evaluation in Reinforcement Learningcited by 26
  4. 2021Inference for Heteroskedastic PCA with Missing Datacited by 21
  5. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  6. 2021Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problemscited by 15
  7. 2022Counterfactual inference in sequential experimentscited by 13
  8. 2022Improved Global Guarantees for the Nonconvex Burer--Monteiro Factorization via Rank Overparameterizationcited by 13
  9. 2022Model-Based Reinforcement Learning for Offline Zero-Sum Markov Gamescited by 11
  10. 2024Low-Rank Contextual Reinforcement Learning from Heterogeneous Human Feedbackcited by 10
  11. 2022Doubly robust nearest neighbors in factor modelscited by 9
  12. 2023Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCAcited by 7
27 more
  1. 2024Concentration properties of fractional posterior in 1-bit matrix completioncited by 7
  2. 2021Learning Treatment Effects in Panels with General Intervention Patternscited by 5
  3. 2023Inference of Dependency Knowledge Graph for Electronic Health Recordscited by 5
  4. 2022Robust Matrix Completion with Heavy-tailed Noisecited by 4
  5. 2022Multi-User Reinforcement Learning with Low Rank Rewardscited by 4
  6. 2026PRISM: Distribution-free Adaptive Computation of Matrix Functions for Accelerating Neural Network Trainingcited by 4
  7. 2024Online Policy Learning and Inference by Matrix Completioncited by 3
  8. 2024LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimationcited by 3
  9. 2023Multi-dimensional domain generalization with low-rank structurescited by 2
  10. 2024Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Informationcited by 2
  11. 2021Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noisecited by 1
  12. 2022Using Interpretable Machine Learning to Massively Increase the Number of Antibody-Virus Interactions Across Studiescited by 1
  13. 2022A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistencycited by 1
  14. 2023Inferences on Mixing Probabilities and Ranking in Mixed-Membership Modelscited by 1
  15. 2021Time-Series Imputation with Wasserstein Interpolation for Optimal Look-Ahead-Bias and Variance Tradeoffcited by 0
  16. 2021Simulation comparisons between Bayesian and de-biased estimators in low-rank matrix completioncited by 0
  17. 2021PAC-Bayesian Matrix Completion with a Spectral Scaled Student Priorcited by 0
  18. 2021Learning to Recommend Using Non-Uniform Datacited by 0
  19. 2022Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithmscited by 0
  20. 2022Uncertainty-Based Non-Parametric Active Peak Detectioncited by 0
  21. 2022A Unified Framework for Estimation of High-dimensional Conditional Factor Modelscited by 0
  22. 2023Misclassification excess risk bounds for 1-bit matrix completioncited by 0
  23. 2024Heterogeneous Treatment Effects in Panel Datacited by 0
  24. 2024Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gapscited by 0
  25. 2024Matrix Completion via Residual Spectral Matchingcited by 0
  26. 2025Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descentcited by 0
  27. 2026Sample-efficient inductive matrix completion with noise and inexact side-informationcited by 0