Smooth Sensitivity Based Approach for Differentially Private Principal Component Analysis
Smooth Sensitivity Based Approach for Differentially Private Principal Component Analysis
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发表时间：
2017-10
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通讯作者：
Alon Gonen;Ran Gilad-Bachrach
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作者：
Alon Gonen;Ran Gilad-Bachrach
目前已知的方法，用于此任务要么采用计算密集的\n {指数机制}或需要访问的协方差矩阵，因此无法利用潜在的稀疏数据。为这一任务设计更简单和更有效的方法的问题已被提出作为一个开放的问题。在本文中，我们解决这个问题，采用输出扰动机制。尽管可以说是最简单和最直接的技术，但由于与发布领先特征向量相关的大的全局敏感性，它一直被忽视。我们解决这个问题，通过采用一个基于平滑敏感性的方法，这使我们能够建立差分隐私（在最坏情况下的方式）和接近最佳的样本复杂性的结果下的特征间隙假设。我们考虑了差分隐私的纯概念和近似概念，并证明了隐私级别和样本复杂度之间的权衡。最后，我们建议我们的结果可以扩展到相关的问题。
Currently known methods for this task either employ the computationally intensive \emph{exponential mechanism} or require an access to the covariance matrix, and therefore fail to utilize potential sparsity of the data. The problem of designing simpler and more efficient methods for this task has been raised as an open problem in \cite{kapralov2013differentially}. In this paper we address this problem by employing the output perturbation mechanism. Despite being arguably the simplest and most straightforward technique, it has been overlooked due to the large \emph{global sensitivity} associated with publishing the leading eigenvector. We tackle this issue by adopting a \emph{smooth sensitivity} based approach, which allows us to establish differential privacy (in a worst-case manner) and near-optimal sample complexity results under eigengap assumption. We consider both the pure and the approximate notions of differential privacy, and demonstrate a tradeoff between privacy level and sample complexity. We conclude by suggesting how our results can be extended to related problems.