Principal component analysis in the stochastic differential privacy model

Fanhua Shang, Zhihui Zhang, Tao Xu, Yuanyuan Liu, Hongying Liu
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1110-1119, 2021.

Abstract

In this paper, we study the differentially private Principal Component Analysis (PCA) problem in stochastic optimization settings. We first propose a new stochastic gradient perturbation PCA mechanism (DP-SPCA) for the calculation of the right singular subspace to achieve $(\epsilon,\delta)$-differential privacy. For achieving a better utility guarantee and performance, we then present a new differential privacy stochastic variance reduction mechanism (DP-VRPCA) with gradient perturbation for PCA. To the best of our knowledge, this is the first work of stochastic gradient perturbation for $(\epsilon,\delta)$-differentially private PCA. We also compare the proposed algorithms with existing state-of-the-art methods, and experiments on real-world datasets and on classification tasks confirm the improved theoretical guarantees of our algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-shang21a, title = {Principal component analysis in the stochastic differential privacy model}, author = {Shang, Fanhua and Zhang, Zhihui and Xu, Tao and Liu, Yuanyuan and Liu, Hongying}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {1110--1119}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/shang21a/shang21a.pdf}, url = {https://proceedings.mlr.press/v161/shang21a.html}, abstract = {In this paper, we study the differentially private Principal Component Analysis (PCA) problem in stochastic optimization settings. We first propose a new stochastic gradient perturbation PCA mechanism (DP-SPCA) for the calculation of the right singular subspace to achieve $(\epsilon,\delta)$-differential privacy. For achieving a better utility guarantee and performance, we then present a new differential privacy stochastic variance reduction mechanism (DP-VRPCA) with gradient perturbation for PCA. To the best of our knowledge, this is the first work of stochastic gradient perturbation for $(\epsilon,\delta)$-differentially private PCA. We also compare the proposed algorithms with existing state-of-the-art methods, and experiments on real-world datasets and on classification tasks confirm the improved theoretical guarantees of our algorithms.} }
Endnote
%0 Conference Paper %T Principal component analysis in the stochastic differential privacy model %A Fanhua Shang %A Zhihui Zhang %A Tao Xu %A Yuanyuan Liu %A Hongying Liu %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-shang21a %I PMLR %P 1110--1119 %U https://proceedings.mlr.press/v161/shang21a.html %V 161 %X In this paper, we study the differentially private Principal Component Analysis (PCA) problem in stochastic optimization settings. We first propose a new stochastic gradient perturbation PCA mechanism (DP-SPCA) for the calculation of the right singular subspace to achieve $(\epsilon,\delta)$-differential privacy. For achieving a better utility guarantee and performance, we then present a new differential privacy stochastic variance reduction mechanism (DP-VRPCA) with gradient perturbation for PCA. To the best of our knowledge, this is the first work of stochastic gradient perturbation for $(\epsilon,\delta)$-differentially private PCA. We also compare the proposed algorithms with existing state-of-the-art methods, and experiments on real-world datasets and on classification tasks confirm the improved theoretical guarantees of our algorithms.
APA
Shang, F., Zhang, Z., Xu, T., Liu, Y. & Liu, H.. (2021). Principal component analysis in the stochastic differential privacy model. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:1110-1119 Available from https://proceedings.mlr.press/v161/shang21a.html.

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