On Perfect Privacy and Maximal Correlation
On Perfect Privacy and Maximal Correlation
复制标题
论完美隐私与最大关联
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Deniz Gündüz
中科院分区：
文献类型：
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作者：
Borzoo Rassouli;Deniz Gündüz
从信息论的角度研究了隐私数据泄露问题。考虑一对相关的随机变量$（X，Y）$，其中$Y$表示观测数据，$X$表示私人潜变量，讨论了以下问题：当不透露关于$X$的信息时，关于$Y$所能透露的最大信息是多少？假设马尔可夫核将Y映射到揭示的信息U，则表明Y和U之间的最大互信息，即，$I（Y;U）$，可以作为标准线性规划的解得到，当要求$X$和$U$独立时，称为 extit{perfect privacy}.该解被证明大于或等于 extit{$Y$携带的关于$X$的非私有信息。}当效用由均方误差的减少$mathbb{E}[（Y-U）^2]$或误差的概率$mbox{Pr}{Y]来衡量时，完全隐私下的最大信息披露也是线性规划的解
eq U}$。对于联合高斯$（X，Y）$，如果内核只应用于$Y$，则完美隐私是不可能的;而如果映射来自$X$和$Y$，则可以实现完美隐私;也就是说，如果私有隐变量也可以在编码器处观察到。其次，分别用$I（Y;U）$和$I（X;U）$度量效用和隐私，研究了当$I（X;U）=0$时，最优效用-隐私权衡曲线的斜率。最后，通过一个类似的，但独立的分析，两个随机变量之间的最大相关性的另一种表征。
The problem of private data disclosure is studied from an information theoretic perspective. Considering a pair of correlated random variables $(X,Y)$, where $Y$ denotes the observed data while $X$ denotes the private latent variables, the following problem is addressed: What is the maximum information that can be revealed about $Y$, while disclosing no information about $X$? Assuming that a Markov kernel maps $Y$ to the revealed information $U$, it is shown that the maximum mutual information between $Y$ and $U$, i.e., $I(Y;U)$, can be obtained as the solution of a standard linear program, when $X$ and $U$ are required to be independent, called extit{perfect privacy}. This solution is shown to be greater than or equal to the extit{non-private information about $X$ carried by $Y$.} Maximal information disclosure under perfect privacy is is shown to be the solution of a linear program also when the utility is measured by the reduction in the mean square error, $mathbb{E}[(Y-U)^2]$, or the probability of error, $mbox{Pr}{Y
eq U}$. For jointly Gaussian $(X,Y)$, it is shown that perfect privacy is not possible if the kernel is applied to only $Y$; whereas perfect privacy can be achieved if the mapping is from both $X$ and $Y$; that is, if the private latent variables can also be observed at the encoder. Next, measuring the utility and privacy by $I(Y;U)$ and $I(X;U)$, respectively, the slope of the optimal utility-privacy trade-off curve is studied when $I(X;U)=0$. Finally, through a similar but independent analysis, an alternative characterization of the maximal correlation between two random variables is provided.