# Distributed Differentially-Private Algorithms for Matrix and Tensor Factorization

arXiv: https://arxiv.org/abs/1804.10299 · HTML: https://mlsanity.com/paper/1804.10299/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2018.

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

- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis](https://mlsanity.com/paper/2108.12373/) (2021)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [CEDAR: Communication Efficient Distributed Analysis for Regressions](https://mlsanity.com/paper/2207.00306/) (2022)
- [Applying Differential Privacy to Tensor Completion](https://mlsanity.com/paper/2110.00539/) (2021)
- [Privacy-Preserving Matrix Factorization for Recommendation Systems using Gaussian Mechanism](https://mlsanity.com/paper/2304.09096/) (2023)
- [Local Differential Privacy with Correlated Noise Achieves Central-DP Optimal Cost](https://mlsanity.com/paper/2605.30476/) (2026)

## Abstract (arXiv)

In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, differentially private algorithms suffer because they introduce noise to guarantee privacy. This paper designs new and improved distributed and differentially private algorithms for two popular matrix and tensor factorization methods: principal component analysis (PCA) and orthogonal tensor decomposition (OTD). The new algorithms employ a correlated noise design scheme to alleviate the effects of noise and can achieve the same noise level as the centralized scenario. Experiments on synthetic and real data illustrate the regimes in which the correlated noise allows performance matching with the centralized setting, outperforming previous methods and demonstrating that meaningful utility is possible while guaranteeing differential privacy.