arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2005.10783cs.ITmath.ITmath.STstat.MLstat.TH
收藏

局部差分隐私下的Fisher信息

Fisher information under local differential privacy

Leighton Pate Barnes, Wei-Ning Chen, Ayfer Ozgur

摘要:

我们开发的数据处理不等式,描述如何从统计样本的Fisher信息可以缩放与隐私参数$\varepsilon$下的本地差分隐私约束。这些界限在统计模型分数分布的一般条件下是有效的,并且它们阐明了在哪些条件下对$\varepsilon$的依赖性是线性的、二次的或指数的。我们展示了这些不等式如何暗示了高斯位置模型和离散分布估计的私人估计的最优下界的所有级别的隐私$\varepsilon>0$。我们进一步将这些不等式应用到稀疏Bernoulli模型中,并证明了具有顺序匹配平方$\ell^2$误差的隐私机制和估计。

英文摘要:

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on $\varepsilon$ is linear, quadratic, or exponential. We show how these inequalities imply order optimal lower bounds for private estimation for both the Gaussian location model and discrete distribution estimation for all levels of privacy $\varepsilon>0$. We further apply these inequalities to sparse Bernoulli models and demonstrate privacy mechanisms and estimators with order-matching squared $\ell^2$ error.

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。

↑