# Fast Differentially Private Matrix Factorization

arXiv: https://arxiv.org/abs/1505.01419 · HTML: https://mlsanity.com/paper/1505.01419/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2015.

## Built on by (most cited first, 20 of 20)

- [Differential Private Knowledge Transfer for Privacy-Preserving Cross-Domain Recommendation](https://mlsanity.com/paper/2202.04893/) (2022)
- [Privately Publishable Per-instance Privacy](https://mlsanity.com/paper/2111.02281/) (2021)
- [Netflix and Forget: Efficient and Exact Machine Unlearning from Bi-linear Recommendations](https://mlsanity.com/paper/2302.06676/) (2023)
- [Private Alternating Least Squares: Practical Private Matrix Completion with Tighter Rates](https://mlsanity.com/paper/2107.09802/) (2021)
- [Modeling Recommender Ecosystems: Research Challenges at the Intersection of Mechanism Design, Reinforcement Learning and Generative Models](https://mlsanity.com/paper/2309.06375/) (2023)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Towards Differential Privacy in Sequential Recommendation: A Noisy Graph Neural Network Approach](https://mlsanity.com/paper/2309.11515/) (2023)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [Private and Utility Enhanced Recommendations with Local Differential Privacy and Gaussian Mixture Model](https://mlsanity.com/paper/2102.13453/) (2021)
- [Privacy-preserving Non-negative Matrix Factorization with Outliers](https://mlsanity.com/paper/2211.01451/) (2022)
- [Privacy-preserving recommender system using the data collaboration analysis for distributed datasets](https://mlsanity.com/paper/2406.01603/) (2024)
- [Privacy-Utility-Bias Trade-offs for Privacy-Preserving Recommender Systems](https://mlsanity.com/paper/2511.22515/) (2025)
- [Fairness-aware Differentially Private Collaborative Filtering](https://mlsanity.com/paper/2303.09527/) (2023)
- [Applying Differential Privacy to Tensor Completion](https://mlsanity.com/paper/2110.00539/) (2021)
- [One-Bit Matrix Completion with Differential Privacy](https://mlsanity.com/paper/2110.00719/) (2021)
- [Introducing the Huber mechanism for differentially private low-rank matrix completion](https://mlsanity.com/paper/2206.07910/) (2022)
- [Decentralized Matrix Factorization with Heterogeneous Differential Privacy](https://mlsanity.com/paper/2212.00306/) (2022)
- [Privacy-Preserving Matrix Factorization for Recommendation Systems using Gaussian Mechanism](https://mlsanity.com/paper/2304.09096/) (2023)
- [Near-Optimal differentially private low-rank trace regression with guaranteed private initialization](https://mlsanity.com/paper/2403.15999/) (2024)
- [One-Sided Matrix Completion from Ultra-Sparse Samples](https://mlsanity.com/paper/2601.12213/) (2026)

## Abstract (arXiv)

Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of differential privacy to Bayesian posterior sampling via Stochastic Gradient Langevin Dynamics. Due to its simplicity the algorithm lends itself to efficient implementation. By careful systems design and by exploiting the power law behavior of the data to maximize CPU cache bandwidth we are able to generate 1024 dimensional models at a rate of 8.5 million recommendations per second on a single PC.