mlsanityData to 7 Oct 2026

Statistical Inferences of Linear Forms for Noisy Matrix Completion

arXiv 1909.00116 ↗First posted 31 Aug 2019math.ST cs.IT cs.LGcited by 18

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Abstract (arXiv)

We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure to construct asymptotically normal estimators of its linear forms through double-sample debiasing and low-rank projection whenever an entry-wise consistent estimator of the matrix is available. These estimators allow us to subsequently construct confidence intervals for and test hypotheses about the linear forms. Our proposal was motivated by a careful perturbation analysis of the empirical singular spaces under the noisy matrix completion model which might be of independent interest. The practical merits of our proposed inference procedure are demonstrated on both simulated and real-world data examples.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Aug 2019.

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Citing papers per year: 2021: 4; 2022: 5; 2023: 1; 2024: 6; 2025: 2.

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  1. 2021Inference for Heteroskedastic PCA with Missing Datacited by 21
  2. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  3. 2024Low-Rank Contextual Reinforcement Learning from Heterogeneous Human Feedbackcited by 10
  4. 2022Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Modelcited by 5
  5. 2022Robust Matrix Completion with Heavy-tailed Noisecited by 4
  6. 2023Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regressioncited by 4
  7. 2024Online Policy Learning and Inference by Matrix Completioncited by 3
  8. 2024Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Informationcited by 2
  9. 2024Low-Rank Online Dynamic Assortment with Dual Contextual Informationcited by 2
  10. 2021Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gapscited by 1
  11. 2021Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noisecited by 1
  12. 2022A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistencycited by 1
6 more
  1. 2022Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithmscited by 0
  2. 2022A Unified Framework for Estimation of High-dimensional Conditional Factor Modelscited by 0
  3. 2024Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gapscited by 0
  4. 2024Matrix Completion via Residual Spectral Matchingcited by 0
  5. 2025Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descentcited by 0
  6. 2025Computational Efficient and Minimax Optimal Nonignorable Matrix Completioncited by 0