We examine the relationship between privacy metrics that utilize information density to measure information leakage between a private and a disclosed random variable. Firstly, we prove that bounding the information density from above or below in turn implies a lower or upper bound on the information density, respectively. Using this result, we establish new relationships between local information privacy, asymmetric local information privacy, pointwise maximal leakage and local differential privacy. We further provide applications of these relations to privacy mechanism design. Furthermore, we provide statements showing the equivalence between a lower bound on information density and risk-averse adversaries. More specifically, we prove an equivalence between a guessing framework and a cost-function framework that result in the desired lower bound on the information density.

翻译：我们研究了利用信息密度衡量私有随机变量与公开随机变量之间信息泄露的隐私度量之间的关系。首先，我们证明对信息密度设定上界或下界，分别意味着对信息密度施加了下界或上界约束。基于这一结论，我们建立了局部信息隐私、非对称局部信息隐私、逐点最大泄露与局部差分隐私之间的新关联，并进一步展示了这些关系在隐私机制设计中的应用。此外，我们给出了信息密度下界与风险规避对手之间等价性的证明。具体而言，我们证明了猜测框架与代价函数框架之间的等价性，这种等价性能够导出所需的信息密度下界。