Distributed Differentially-Private Algorithms for Matrix and Tensor Factorization
This work addresses privacy concerns for signal processing and machine learning applications where data is distributed across locations, offering improved utility while ensuring differential privacy.
The paper tackled the problem of preserving privacy in distributed matrix and tensor factorization by designing new differentially private algorithms for PCA and orthogonal tensor decomposition, achieving noise levels comparable to centralized settings and outperforming previous methods in experiments.
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.