# Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information

arXiv: https://arxiv.org/abs/2403.14899 · HTML: https://mlsanity.com/paper/2403.14899/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Statistical Inferences of Linear Forms for Noisy Matrix Completion](https://mlsanity.com/paper/1909.00116/) (2019)
- [Collective Matrix Completion](https://mlsanity.com/paper/1807.09010/) (2018)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Sparse network asymptotics for logistic regression](https://mlsanity.com/paper/2010.04703/) (2020)

## Built on by (most cited first, 2 of 2)

- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)

## Abstract (arXiv)

This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the covariates, and allow its probability to go to zero as the sample size increases. We apply an iterative least squares (LS) estimation approach in our considered context. The iterative LS methods in general enjoy a low computational cost, but deriving the statistical properties of the resulting estimators is a challenging task. We show that our method only needs a few iterations, and the resulting entry-wise estimators of the low-rank matrix and the coefficient matrix are guaranteed to have asymptotic normal distributions. As a result, individual inference can be conducted for each entry of the unknown matrices. We also propose a simultaneous testing procedure with multiplier bootstrap for the high-dimensional coefficient matrix. This simultaneous inferential tool can help us further investigate the effects of covariates for the prediction of missing entries.