Distributed Differentially-Private Algorithms for Matrix and Tensor Factorization

TL;DR

This paper introduces new distributed differentially private algorithms for matrix and tensor factorizations, specifically PCA and OTD, that reduce noise impact and match centralized performance.

Contribution

It proposes correlated noise schemes for distributed DP algorithms, improving utility and outperforming previous methods in PCA and OTD.

Findings

Achieves centralized-level utility with distributed DP algorithms.

Outperforms previous methods in synthetic and real data experiments.

Demonstrates meaningful privacy-utility trade-offs.

Abstract

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.