# Introducing the Huber mechanism for differentially private low-rank matrix completion

arXiv: https://arxiv.org/abs/2206.07910 · HTML: https://mlsanity.com/paper/2206.07910/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Low-Rank Matrix Completion: A Contemporary Survey](https://mlsanity.com/paper/1907.11705/) (2019)
- [Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm](https://mlsanity.com/paper/1510.06895/) (2015)
- [Fast Differentially Private Matrix Factorization](https://mlsanity.com/paper/1505.01419/) (2015)
- [Iteratively Reweighted Least Squares for Basis Pursuit with Global Linear Convergence Rate](https://mlsanity.com/paper/2012.12250/) (2020)
- [Private Alternating Least Squares: Practical Private Matrix Completion with Tighter Rates](https://mlsanity.com/paper/2107.09802/) (2021)
- [Differentially Private Matrix Completion Revisited](https://mlsanity.com/paper/1712.09765/) (2017)
- [SweetRS: Dataset for a recommender systems of sweets](https://mlsanity.com/paper/1709.03496/) (2017)

## Abstract (arXiv)

Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired by Huber loss, a well-known loss function in robust statistics. The proposed Huber mechanism is evaluated against existing differential privacy mechanisms while solving the matrix completion problem using the Alternating Least Squares approach. We also propose using the Iteratively Re-Weighted Least Squares algorithm to complete low-rank matrices and study the performance of different noise mechanisms in both synthetic and real datasets. We prove that the proposed mechanism achieves ε-differential privacy similar to the Laplace mechanism. Furthermore, empirical results indicate that the Huber mechanism outperforms Laplacian and Gaussian in some cases and is comparable, otherwise.