# Matrix Completion with Noisy Entries and Outliers

arXiv: https://arxiv.org/abs/1503.00214 · HTML: https://mlsanity.com/paper/1503.00214/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2015.

## Built on by (most cited first, 7 of 7)

- [Robust Matrix Completion with Heavy-tailed Noise](https://mlsanity.com/paper/2206.04276/) (2022)
- [Square Root Principal Component Pursuit: Tuning-Free Noisy Robust Matrix Recovery](https://mlsanity.com/paper/2106.09211/) (2021)
- [Discrete Aware Matrix Completion via Convexized ℓ0-Norm Approximation](https://mlsanity.com/paper/2405.02101/) (2024)
- [Tailed Low-Rank Matrix Factorization for Similarity Matrix Completion](https://mlsanity.com/paper/2409.19550/) (2024)
- [Alternating minimization for square root principal component pursuit](https://mlsanity.com/paper/2501.00471/) (2024)
- [RGNMR: A Gauss-Newton method for robust matrix completion with theoretical guarantees](https://mlsanity.com/paper/2505.12919/) (2025)
- [Low Rank Tensor Completion via Adaptive ADMM](https://mlsanity.com/paper/2605.03736/) (2026)

## Abstract (arXiv)

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting.