Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems

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Jason Ge, Zhaoran Wang, Mengdi Wang, Han Liu ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1589-1598, 2018.

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.

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