Bounds on Maximal Leakage over Bayesian Networks
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917165308837888 |
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| author | Makur, Anuran Singh, Japneet |
| author_facet | Makur, Anuran Singh, Japneet |
| contents | Maximal leakage quantifies the leakage of information from data $X \in \mathcal{X}$ due to an observation $Y$. While fundamental properties of maximal leakage, such as data processing, sub-additivity, and its connection to mutual information, are well-established, its behavior over Bayesian networks is not well-understood and existing bounds are primarily limited to binary $\mathcal{X}$. In this paper, we investigate the behavior of maximal leakage over Bayesian networks with finite alphabets. Our bounds on maximal leakage are established by utilizing coupling-based characterizations which exist for channels satisfying certain conditions. Furthermore, we provide more general conditions under which such coupling characterizations hold for $|\mathcal{X}| = 4$. In the course of our analysis, we also present a new simultaneous coupling result on maximal leakage exponents. Finally, we illustrate the effectiveness of the proposed bounds with some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on Maximal Leakage over Bayesian Networks Makur, Anuran Singh, Japneet Information Theory Probability Statistics Theory Maximal leakage quantifies the leakage of information from data $X \in \mathcal{X}$ due to an observation $Y$. While fundamental properties of maximal leakage, such as data processing, sub-additivity, and its connection to mutual information, are well-established, its behavior over Bayesian networks is not well-understood and existing bounds are primarily limited to binary $\mathcal{X}$. In this paper, we investigate the behavior of maximal leakage over Bayesian networks with finite alphabets. Our bounds on maximal leakage are established by utilizing coupling-based characterizations which exist for channels satisfying certain conditions. Furthermore, we provide more general conditions under which such coupling characterizations hold for $|\mathcal{X}| = 4$. In the course of our analysis, we also present a new simultaneous coupling result on maximal leakage exponents. Finally, we illustrate the effectiveness of the proposed bounds with some examples. |
| title | Bounds on Maximal Leakage over Bayesian Networks |
| topic | Information Theory Probability Statistics Theory |
| url | https://arxiv.org/abs/2512.04955 |