# One-Bit Matrix Completion with Differential Privacy

arXiv: https://arxiv.org/abs/2110.00719 · HTML: https://mlsanity.com/paper/2110.00719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 61 references that are in the map.
- First posted on arXiv 2 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Efficient Private ERM for Smooth Objectives](https://mlsanity.com/paper/1703.09947/) (2017)
- [PU Learning for Matrix Completion](https://mlsanity.com/paper/1411.6081/) (2014)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Fast Differentially Private Matrix Factorization](https://mlsanity.com/paper/1505.01419/) (2015)
- [Deep Item-based Collaborative Filtering for Top-N Recommendation](https://mlsanity.com/paper/1811.04392/) (2018)
- [1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation](https://mlsanity.com/paper/1604.04191/) (2016)
- [1-Bit Matrix Completion under Exact Low-Rank Constraint](https://mlsanity.com/paper/1502.06689/) (2015)
- [A divide-and-conquer algorithm for binary matrix completion](https://mlsanity.com/paper/1907.04251/) (2019)

## Abstract (arXiv)

As a prevailing collaborative filtering method for recommendation systems, one-bit matrix completion requires data collected by users to provide personalized service. Due to insidious attacks and unexpected inference, the release of users' data often raises serious privacy concerns. To address this issue, differential privacy(DP) has been widely used in standard matrix completion models. To date, however, little has been known about how to apply DP to achieve privacy protection in one-bit matrix completion. In this paper, we propose a unified framework for ensuring a strong privacy guarantee of one-bit matrix completion with DP. In our framework, we develop four different private perturbation mechanisms corresponding to different stages of one-bit matrix completion. For each mechanism, we design a privacy-preserving algorithm and provide a theoretical recovery error bound under the proper conditions. Numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposal. Compared to the one-bit matrix completion without privacy protection, our proposed mechanisms can maintain high-level privacy protection with marginal loss of completion accuracy.