Several Representations of $α$-Mutual Information and Interpretations as Privacy Leakage Measures
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916713908404224 |
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| author | Kamatsuka, Akira Yoshida, Takashiro |
| author_facet | Kamatsuka, Akira Yoshida, Takashiro |
| contents | In this paper, we present several novel representations of $α$-mutual information ($α$-MI) in terms of R{\' e}nyi divergence and conditional R{\' e}nyi entropy. The representations are based on the variational characterizations of $α$-MI using a reverse channel. Based on these representations, we provide several interpretations of the $α$-MI as privacy leakage measures using generalized mean and gain functions. Further, as byproducts of the representations, we propose novel conditional R{\' e}nyi entropies that satisfy the property that conditioning reduces entropy and data-processing inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Several Representations of $α$-Mutual Information and Interpretations as Privacy Leakage Measures Kamatsuka, Akira Yoshida, Takashiro Information Theory In this paper, we present several novel representations of $α$-mutual information ($α$-MI) in terms of R{\' e}nyi divergence and conditional R{\' e}nyi entropy. The representations are based on the variational characterizations of $α$-MI using a reverse channel. Based on these representations, we provide several interpretations of the $α$-MI as privacy leakage measures using generalized mean and gain functions. Further, as byproducts of the representations, we propose novel conditional R{\' e}nyi entropies that satisfy the property that conditioning reduces entropy and data-processing inequality. |
| title | Several Representations of $α$-Mutual Information and Interpretations as Privacy Leakage Measures |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.10099 |