For $\tilde{f}(t) = \exp(\frac{\alpha-1}{\alpha}t)$, this paper proposes a $\tilde{f}$-mean information gain measure. R\'{e}nyi divergence is shown to be the maximum $\tilde{f}$-mean information gain incurred at each elementary event $y$ of channel output $Y$ and Sibson mutual information is the $\tilde{f}$-mean of this $Y$-elementary information gain. Both are proposed as $\alpha$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $\alpha$-leakage by Arimoto mutual information can be expressed as $\tilde{f}$-mean measures by a scaled probability. Further, Sibson mutual information is interpreted as the maximum $\tilde{f}$-mean information gain over all estimation decisions applied to channel output. This reveals that the exiting generalized Blahut-Arimoto method for computing R\'{e}nyi capacity (or Gallager's error exponent) in fact maximizes a $\tilde{f}$-mean information gain iteratively over estimation decision and channel input. This paper also derives a decomposition of $\tilde{f}$-mean information gain, analogous to the Sibson identity for R\'{e}nyi divergence.

翻译：对于$\tilde{f}(t) = \exp(\frac{\alpha-1}{\alpha}t)$，本文提出一种$\tilde{f}$均值信息增益度量。研究表明，Rényi散度是信道输出$Y$的每个基本事件$y$上所产生的最大$\tilde{f}$均值信息增益，而Sibson互信息则是这种$Y$基本事件信息增益的$\tilde{f}$均值。两者均被提出作为α-泄漏量度量，用于指示攻击者可能获取敏感数据的最大信息量。研究进一步表明，现有基于Arimoto互信息的α-泄漏量可通过缩放概率表示为$\tilde{f}$均值度量形式。此外，Sibson互信息被解释为对信道输出施加所有估计决策时的最大$\tilde{f}$均值信息增益。这一发现揭示了现有用于计算Rényi容量（或Gallager错误指数）的广义Blahut-Arimoto方法，实际上是在估计决策与信道输入之间迭代优化一个$\tilde{f}$均值信息增益。本文还推导了$\tilde{f}$均值信息增益的分解形式，该分解与Rényi散度的Sibson恒等式具有类似结构。