arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2009.02668cs.LGcs.CRcs.DSstat.ML
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私有矩阵分析框架

A Framework for Private Matrix Analysis

Johns Hopkins University(约翰霍普金斯大学);Fujitsu Laboratories of America(富士通美国研究院)

Jalaj Upadhyay, Sarvagya Upadhyay

摘要:

我们研究了滑动窗口模型中的私有矩阵分析,其中只有最后的$W$更新矩阵被认为是有用的分析。我们给第一个有效的$o(W)$空间差分私有算法的频谱近似,主成分分析,线性回归。我们还启动和显示有效的差异私有算法的两个重要的主成分分析:稀疏主成分分析和非负主成分分析。在我们的工作之前,即使在静态数据设置中,稀疏和非负差分私有主成分分析也没有这样的结果。这些算法是通过确定由流矩阵构成半正定矩阵的充分条件而得到的。我们还显示了计算低秩近似所需的空间上的下界,即使该算法给出了乘法近似,并引起附加误差。这通过减少到某个通信复杂性问题而实现。

英文摘要:

We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation, principal component analysis, and linear regression. We also initiate and show efficient differentially private algorithms for two important variants of principal component analysis: sparse principal component analysis and non-negative principal component analysis. Prior to our work, no such result was known for sparse and non-negative differentially private principal component analysis even in the static data setting. These algorithms are obtained by identifying sufficient conditions on positive semidefinite matrices formed from streamed matrices. We also show a lower bound on space required to compute low-rank approximation even if the algorithm gives multiplicative approximation and incurs additive error. This follows via reduction to a certain communication complexity problem.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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