$\alpha$-leakage by R\'enyi Divergence and Sibson Mutual Information
<|reference_start|>$\alpha$-leakage by R\'enyi Divergence and Sibson Mutual Information: 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.<|reference_end|>
@article{ding2024$\alpha$-leakage,
    title={$\alpha$-leakage by R\'{e}nyi Divergence and Sibson Mutual Information},
    author={Ni Ding, Mohammad Amin Zarrabian, Parastoo Sadeghi},
    journal={arXiv preprint arXiv:2405.00423},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00423},
    primaryClass={cs.IT math.IT}
}