Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems
Jason Ge, Zhaoran Wang, Mengdi Wang, Han Liu
Abstract
This paper proposes a distributed privacy-preserving sparse PCA (DPS-PCA) algorithm that generates a minimax-optimal sparse PCA estimator under differential privacy constraints. In a distributed optimization framework, data providers can use this algorithm to collaboratively analyze the union of their data sets while limiting the disclosure of their private information. DPS-PCA can recover the leading eigenspace of the population covariance at a geometric convergence rate, and simultaneously achieves the optimal minimax statistical error for high-dimensional data. Our algorithm provides fine-tuned control over the tradeoff between estimation accuracy and privacy preservation. Numerical simulations demonstrate that DPS-PCA significantly outperforms other privacy-preserving PCA methods in terms of estimation accuracy and computational efficiency.
BibTeX
@InProceedings{pmlr-v84-ge18a,
title = {Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems},
author = {Ge, Jason and Wang, Zhaoran and Wang, Mengdi and Liu, Han},
booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
pages = {1589--1598},
year = {2018},
editor = {Storkey, Amos and Perez-Cruz, Fernando},
volume = {84},
series = {Proceedings of Machine Learning Research},
month = {09--11 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v84/ge18a/ge18a.pdf},
url = {https://proceedings.mlr.press/v84/ge18a.html},
abstract = {This paper proposes a distributed privacy-preserving sparse PCA (DPS-PCA) algorithm that generates a minimax-optimal sparse PCA estimator under differential privacy constraints. In a distributed optimization framework, data providers can use this algorithm to collaboratively analyze the union of their data sets while limiting the disclosure of their private information. DPS-PCA can recover the leading eigenspace of the population covariance at a geometric convergence rate, and simultaneously achieves the optimal minimax statistical error for high-dimensional data. Our algorithm provides fine-tuned control over the tradeoff between estimation accuracy and privacy preservation. Numerical simulations demonstrate that DPS-PCA significantly outperforms other privacy-preserving PCA methods in terms of estimation accuracy and computational efficiency.}
}