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arXiv 1906.03049stat.MLcs.CRcs.LG
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利用FFT计算严格差分隐私保证

Computing Tight Differential Privacy Guarantees Using FFT

Helsinki Institute for Information Technology HIIT(赫尔辛基信息技术研究所);University of Helsinki(赫尔辛基大学);Aalto University(阿尔托大学)

Antti Koskela, Joonas Jälkö, Antti Honkela

摘要:

差分私有(DP)机器学习最近变得流行。DP算法的隐私丢失通常使用$(\varepsilon,δ)$ -DP报告。在本文中,我们提出了一个数值会计评估算法的隐私损失与连续一维输出。这种会计可以应用于下采样多维高斯机制,这是流行的DP随机梯度下降。所提出的方法是基于数值近似的积分公式,它给出了确切的$(\varepsilon,δ)$值。通过离散积分和使用快速傅立叶变换算法评估离散卷积来进行近似。我们给出了理论误差界和数值误差估计的近似。与最先进的技术的实验比较表明,显着改善绑定紧密性和/或计算时间。该方法的Python代码可以在Github(https://github.com/DPBayes/PLD-Accounting/)中找到。

英文摘要:

Differentially private (DP) machine learning has recently become popular. The privacy loss of DP algorithms is commonly reported using $(\varepsilon,δ)$-DP. In this paper, we propose a numerical accountant for evaluating the privacy loss for algorithms with continuous one dimensional output. This accountant can be applied to the subsampled multidimensional Gaussian mechanism which underlies the popular DP stochastic gradient descent. The proposed method is based on a numerical approximation of an integral formula which gives the exact $(\varepsilon,δ)$-values. The approximation is carried out by discretising the integral and by evaluating discrete convolutions using the fast Fourier transform algorithm. We give both theoretical error bounds and numerical error estimates for the approximation. Experimental comparisons with state-of-the-art techniques demonstrate significant improvements in bound tightness and/or computation time. Python code for the method can be found in Github (https://github.com/DPBayes/PLD-Accountant/).

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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