# Statistical Inferences of Linear Forms for Noisy Matrix Completion

arXiv: https://arxiv.org/abs/1909.00116 · HTML: https://mlsanity.com/paper/1909.00116/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2019.

## Built on by (most cited first, 18 of 18)

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- [Robust Matrix Completion with Heavy-tailed Noise](https://mlsanity.com/paper/2206.04276/) (2022)
- [Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression](https://mlsanity.com/paper/2305.06199/) (2023)
- [Online Policy Learning and Inference by Matrix Completion](https://mlsanity.com/paper/2404.17398/) (2024)
- [Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information](https://mlsanity.com/paper/2403.14899/) (2024)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gaps](https://mlsanity.com/paper/2104.03298/) (2021)
- [Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noise](https://mlsanity.com/paper/2110.12046/) (2021)
- [A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency](https://mlsanity.com/paper/2211.09272/) (2022)
- [Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps](https://mlsanity.com/paper/2410.11225/) (2024)
- [Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms](https://mlsanity.com/paper/2202.04061/) (2022)
- [A Unified Framework for Estimation of High-dimensional Conditional Factor Models](https://mlsanity.com/paper/2209.00391/) (2022)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)
- [Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent](https://mlsanity.com/paper/2501.13385/) (2025)
- [Computational Efficient and Minimax Optimal Nonignorable Matrix Completion](https://mlsanity.com/paper/2504.04016/) (2025)

## 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.