非零漏损和不可逆漏损矩阵的数据披露
Data Disclosure with Non-zero Leakage and Non-invertible Leakage Matrix
摘要：
我们研究的统计信号处理隐私问题，代理观察有用的数据$Y$，并希望透露给用户的信息。由于有用数据与私有数据$X$相关，所以代理采用隐私机制来生成可以被发布的数据$U$。我们研究了隐私机制的设计，最大限度地提高了$Y$的信息，同时满足一个强大的$\ell_1$隐私标准。当允许足够小的泄漏时，我们表明隐私机制设计问题的优化器向量具有特定的几何形状，即，它们是固定向量分布的扰动。这种几何结构允许我们使用条件熵的局部近似。利用这种近似方法，可以将原优化问题转化为一个线性规划问题，从而可以很容易地得到隐私机制的近似解。这项工作的主要贡献是考虑非零泄漏与不可逆的泄漏矩阵。在一个受水印应用启发的例子中，我们首先研究了近似的精度。然后，我们采用不同的措施，效用和隐私泄漏比较隐私效用权衡使用我们的方法与其他方法。特别是，它已被证明，通过允许小的泄漏，显着的效用，可以实现使用我们的方法相比，不允许泄漏的情况下。
英文摘要：
We study a statistical signal processing privacy problem, where an agent observes useful data $Y$ and wants to reveal the information to a user. Since the useful data is correlated with the private data $X$, the agent employs a privacy mechanism to generate data $U$ that can be released. We study the privacy mechanism design that maximizes the revealed information about $Y$ while satisfying a strong $\ell_1$-privacy criterion. When a sufficiently small leakage is allowed, we show that the optimizer vectors of the privacy mechanism design problem have a specific geometry, i.e., they are perturbations of fixed vector distributions. This geometrical structure allows us to use a local approximation of the conditional entropy. By using this approximation the original optimization problem can be reduced to a linear program so that an approximate solution for privacy mechanism can be easily obtained. The main contribution of this work is to consider non-zero leakage with a non-invertible leakage matrix. In an example inspired by water mark application, we first investigate the accuracy of the approximation. Then, we employ different measures for utility and privacy leakage to compare the privacy-utility trade-off using our approach with other methods. In particular, it has been shown that by allowing small leakage, significant utility can be achieved using our method compared to the case where no leakage is allowed.
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