{"ID":2833075,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.04955","arxiv_id":"2512.04955","title":"Bounds on Maximal Leakage over Bayesian Networks","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.","short_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-underst...","url_abs":"https://arxiv.org/abs/2512.04955","url_pdf":"https://arxiv.org/pdf/2512.04955v1","authors":"[\"Anuran Makur\",\"Japneet Singh\"]","published":"2025-12-04T16:25:21Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}