Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems %A Jason Ge %A Zhaoran Wang %A Mengdi Wang %A Han Liu %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-ge18a %I PMLR %P 1589--1598 %U https://proceedings.mlr.press/v84/ge18a.html %V 84 %X 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.
APA
Ge, J., Wang, Z., Wang, M. & Liu, H.. (2018). Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1589-1598 Available from https://proceedings.mlr.press/v84/ge18a.html.

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