The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A statistical privacy mechanism is employed to generate data $U$ based on $(X,Y)$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. To this end, we use extended versions of the Functional Representation Lemma and Strong Functional Representation Lemma and combine them with a simple observation which we call separation technique. New lower bounds on privacy-utility trade-off are derived and we show that they can improve the previous bounds. We study the obtained bounds in different scenarios and compare them with previous results.

翻译：本文研究统计信号处理中的隐私问题设计，假设私有数据是可观测的。在该工作中，智能体观测到与私有数据 $X$ 相关且有用的数据 $Y$，并希望向用户披露有用信息。通过基于 $(X,Y)$ 生成数据 $U$ 的统计隐私机制，在满足隐私准则的同时最大化关于 $Y$ 的披露信息。为此，我们采用函数表示引理和强函数表示引理的扩展版本，并将其与称为分离技术的简单观测相结合。推导出隐私-效用权衡的新下界，并证明其可改善先前的界。我们研究了不同场景下所得到的界，并与先前结果进行了比较。