# Robust matrix completion via Novel M-estimator Functions

arXiv: https://arxiv.org/abs/2310.04953 · HTML: https://mlsanity.com/paper/2310.04953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Builds on (most cited first, 4 of 4)

- [Global Optimality in Low-rank Matrix Optimization](https://mlsanity.com/paper/1702.07945/) (2017)
- [The Global Optimization Geometry of Low-Rank Matrix Optimization](https://mlsanity.com/paper/1703.01256/) (2017)
- [Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix Estimation](https://mlsanity.com/paper/1802.08397/) (2018)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)

## Abstract (arXiv)

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and ℓp-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.