We explore a family of information measures that stems from R\'enyi's $\alpha$-Divergences with $\alpha<0$. In particular, we extend the definition of Sibson's $\alpha$-Mutual Information to negative values of $\alpha$ and show several properties of these objects. Moreover, we highlight how this family of information measures is related to functional inequalities that can be employed in a variety of fields, including lower-bounds on the Risk in Bayesian Estimation Procedures.

翻译：我们探讨一套由R\'enyi$\alpha$-Diverences(以美元计算)产生的信息计量方法。我们特别将Sibson$\alpha$-mutual Information的定义扩大到负值$\alpha$-mutual Information(以美元计算),并展示了这些物体的几种特性。此外,我们强调这一信息计量方法如何与各领域可以采用的功能不平等有关,包括巴耶西亚模拟程序风险的下限。