arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2306.01751cs.CRcs.LGstat.ML
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结合随机投影与符号随机投影的差分隐私

Differential Privacy with Random Projections and Sign Random Projections

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Ping Li, Xiaoyun Li

AI总结:

该研究基于随机投影与符号随机投影开发系列差分隐私算法,提出平滑翻转概率技术优化位翻转策略,构建的DP-SignOPORP、iDP-SignRP在不同隐私设定下均实现了效用提升。

摘要:

本文针对机器学习、数据挖掘和信息检索领域的通用应用场景,基于一类随机投影(RP)族开发了一系列差分隐私(DP)算法。在提出的算法中,iDP-SignRP在“个体差分隐私”(iDP)设定下效果显著,其核心基于符号随机投影(SignRP)构建。此外,DP-SignOPORP采用“一次排列+一次随机投影”(OPORP)结构,在标准DP设定下大幅优于现有文献中的算法;其中OPORP是经典count-sketch方法的变体,引入了定长分箱与归一化操作。若不进行符号提取,在DP-RP算法族中,DP-OPORP的性能表现最优。\n我们改进DP-RP的核心思路是仅保留投影后数据的符号,即$sign(x_j) = sign\left(\sum_{i=1}^p u_i w_{ij}\right)$。其核心直觉在于:当原始数据($u$)发生微小变化时(符合DP中“邻居”的定义),投影后的符号通常保持不变。换言之,聚合与量化操作本身就能提供良好的隐私保护效果。我们提出了“平滑翻转概率”技术,该技术利用了SignRP的这一固有隐私优势,对标准DP位翻转策略进行了优化。基于该技术,我们提出的DP-SignOPORP满足严格的DP要求,且性能优于其他基于SignRP(及RP)的DP变体,尤其在$ε$不太大的场景下(例如$ε= 5\sim10$)效果更突出。此外,如果应用场景可接受个体DP,我们还可直接得到iDP-SignRP算法,该算法即使在$ε$很小的情况下(例如$ε<0.5$)也能实现极佳的效用。

英文摘要:

In this paper, we develop a series of differential privacy (DP) algorithms from a family of random projections (RP) for general applications in machine learning, data mining, and information retrieval. Among the presented algorithms, iDP-SignRP is remarkably effective under the setting of ``individual differential privacy'' (iDP), based on sign random projections (SignRP). Also, DP-SignOPORP considerably improves existing algorithms in the literature under the standard DP setting, using ``one permutation + one random projection'' (OPORP), where OPORP is a variant of the celebrated count-sketch method with fixed-length binning and normalization. Without taking signs, among the DP-RP family, DP-OPORP achieves the best performance. Our key idea for improving DP-RP is to take only the signs, i.e., $sign(x_j) = sign\left(\sum_{i=1}^p u_i w_{ij}\right)$, of the projected data. The intuition is that the signs often remain unchanged when the original data ($u$) exhibit small changes (according to the ``neighbor'' definition in DP). In other words, the aggregation and quantization operations themselves provide good privacy protections. We develop a technique called ``smooth flipping probability'' that incorporates this intuitive privacy benefit of SignRPs and improves the standard DP bit flipping strategy. Based on this technique, we propose DP-SignOPORP which satisfies strict DP and outperforms other DP variants based on SignRP (and RP), especially when $ε$ is not very large (e.g., $ε= 5\sim10$). Moreover, if an application scenario accepts individual DP, then we immediately obtain an algorithm named iDP-SignRP which achieves excellent utilities even at small~$ε$ (e.g., $ε<0.5$).

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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