Bounds on Maximal Leakage over Bayesian Networks

Anuran Makur; Japneet Singh

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arXiv · 2512.04955

Bounds on Maximal Leakage over Bayesian Networks

Anuran Makur·Japneet Singh

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Abstract

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.

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Anuran Makur, Japneet Singh. 2025-12-04. Bounds on Maximal Leakage over Bayesian Networks. https://arxiv.org/abs/2512.04955

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