Principal Component Analysis in the local differential privacy model

被引:14
|
作者
Wang, Di [1 ]
Xu, Jinhui [1 ]
机构
[1] SUNY Buffalo, Dept Comp Sci & Engn, 338 Davis Hall, Buffalo, NY 14260 USA
关键词
Local differential privacy; Principal Component Analysis; Sparse PCA;
D O I
10.1016/j.tcs.2019.12.019
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In this paper, we study the Principal Component Analysis (PCA) problem under the (distributed) non-interactive local differential privacy model. For the low dimensional case (i.e., p << n), we show the optimal rate of Theta(kp/n epsilon(2)) (omitting the eigenvalue terms) for the private minimax risk of the k-dimensional PCA using the squared subspace distance as the measurement, where n is the sample size and E is the privacy parameter. For the high dimensional (i.e., p >> n) row sparse case, we first give a lower bound of Omega(ks log p/n epsilon(2))) on the private minimax risk, where s is the underlying sparsity parameter. Then we provide an efficient algorithm to achieve the upper bound of O(s(2) log p/n epsilon(2)). Experiments on both synthetic and real world datasets confirm our theoretical guarantees. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码:296 / 312
页数:17
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