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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.14304 |
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| _version_ | 1866911927576297472 |
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| author | Kamatsuka, Akira Kazama, Koki Yoshida, Takahiro |
| author_facet | Kamatsuka, Akira Kazama, Koki Yoshida, Takahiro |
| contents | $H$-mutual information ($H$-MI) is a wide class of information leakage measures, where $H=(η, F)$ is a pair of monotonically increasing function $η$ 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 $α$, $g$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Variational Characterization of $H$-Mutual Information and its Application to Computing $H$-Capacity Kamatsuka, Akira Kazama, Koki Yoshida, Takahiro Information Theory $H$-mutual information ($H$-MI) is a wide class of information leakage measures, where $H=(η, F)$ is a pair of monotonically increasing function $η$ 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 $α$, $g$-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. |
| title | A Variational Characterization of $H$-Mutual Information and its Application to Computing $H$-Capacity |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.14304 |