A Variational Characterization of $H$-Mutual Information and its Application to Computing $H$-Capacity
<|reference_start|>A Variational Characterization of $H$-Mutual Information and its Application to Computing $H$-Capacity: $H$-mutual information ($H$-MI) is a wide class of information leakage measures, where $H=(\eta, F)$ is a pair of monotonically increasing function $\eta$ and a concave function $F$, which is a generalization of Shannon entropy. $H$-MI is defined as the difference between the generalized entropy $H$ and its conditional version, including Shannon mutual information (MI), Arimoto MI of order $\alpha$, $g$-leakage, and expected value of sample information. This study presents a variational characterization of $H$-MI via statistical decision theory. Based on the characterization, we propose an alternating optimization algorithm for computing $H$-capacity.<|reference_end|>
@article{kamatsuka2024a,
    title={A Variational Characterization of $H$-Mutual Information and its
  Application to Computing $H$-Capacity},
    author={Akira Kamatsuka, Koki Kazama, Takahiro Yoshida},
    journal={arXiv preprint arXiv:2406.14304},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14304},
    primaryClass={cs.IT math.IT}
}