ArticleProceedings of the National Academy of Sciences of the United States of America2019
Inference and uncertainty quantification for noisy matrix completion.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 19 papers.
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Who cites it
19 citing papers in PubMed.
- LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation.Statistics in medicine · 2026Article
- Inference of dependency knowledge graph for Electronic Health Records.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2026Article
- Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference.Journal of the American Statistical Association · 2026Article
- COUNTERFACTUAL INFERENCE IN SEQUENTIAL EXPERIMENTS.Annals of statistics · 2025Article
- AUGMENTED DOUBLY ROBUST POST-IMPUTATION INFERENCE FOR PROTEOMIC DATA.The annals of applied statistics · 2025Article
- AUGMENTED DOUBLY ROBUST POST-IMPUTATION INFERENCE FOR PROTEOMIC DATA.bioRxiv : the preprint server for biology · 2025Article
- Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models.Journal of the American Statistical Association · 2024Article
- Using interpretable machine learning to extend heterogeneous antibody-virus datasets.Cell reports methods · 2023Article
- Matrix completion under complex survey sampling.Annals of the Institute of Statistical Mathematics · 2023Article
- Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution under Random Designs.Journal of the American Statistical Association · 2023Article
- Uncertainty in denoising of MRSI using low-rank methods.Magnetic resonance in medicine · 2022Article
- Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problems.Proceedings of the ... International Conference on Machine Learning and Applications. International Conference on Machine Learning and Applications · 2021Article
- BRIDGING CONVEX AND NONCONVEX OPTIMIZATION IN ROBUST PCA: NOISE, OUTLIERS, AND MISSING DATA.Annals of statistics · 2021Article
- A SHRINKAGE PRINCIPLE FOR HEAVY-TAILED DATA: HIGH-DIMENSIONAL ROBUST LOW-RANK MATRIX RECOVERY.Annals of statistics · 2021Article
- ASYMMETRY HELPS: EIGENVALUE AND EIGENVECTOR ANALYSES OF ASYMMETRICALLY PERTURBED LOW-RANK MATRICES.Annals of statistics · 2021Article
- RankSIAM journal on mathematics of data science · 2021Article
- A Note on Exploratory Item Factor Analysis by Singular Value Decomposition.Psychometrika · 2020Article
- NOISY MATRIX COMPLETION: UNDERSTANDING STATISTICAL GUARANTEES FOR CONVEX RELAXATION VIA NONCONVEX OPTIMIZATION.SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics · 2020Article
- Comment: Feature Screening and Variable Selection via Iterative Ridge Regression.Technometrics : a journal of statistics for the physical, chemical, and engineering sciences · 2020Article
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4 authors.
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Abstract
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.
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