论文标题
强烈的$χ^2 $私有数据披露的设计框架
A Design Framework for Strongly $χ^2$-Private Data Disclosure
论文作者
论文摘要
在本文中，我们使用信息理论方法研究了随机披露控制问题。要披露的有用数据取决于应保护的私人数据。因此，我们设计了一种隐私机制来生成新数据，该数据在强$χ^2 $ - 私有化标准下最大化有关有用数据的披露信息。对于足够小的泄漏，可以通过互相近似的局部近似值在概率分布的空间中对隐私机制设计问题进行几何研究。通过使用欧几里得信息几何形状中的方法，可以将原始高度挑战性的优化问题缩小为找到矩阵的主要右旋向量的问题，该矩阵的主要右旋向量是最佳隐私机制的特征。在两次扩展中，我们首先考虑一个场景，其中对手会收到用户消息的嘈杂版本，然后我们寻找一种机制，该机制基于观察$ x $，找到$ u $ $ $ $，从而最大化$ u $和$ y $之间的共同信息，同时满足$ $ u $ $ $ $ y $ y $ y $和$ z $ z $ $ $ $ $ y $ y＆z $ z $下的Markov Chain Chain $（Z，Z，Z，Y）。
In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong $χ^2$-privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds $U$ based on observing $X$, maximizing the mutual information between $U$ and $Y$ while satisfying the privacy criterion on $U$ and $Z$ under the Markov chain $(Z,Y)-X-U$.
