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Bounds on the Posterior-to-Prior Ratios for Inclusion Belief under Bounded Differential Privacy — arXiv:2608.30473

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.30473
License (as archived): CC0-1.0
Archived: 2026-10-17T08:27:57.432Z
SHA-256 of the archived text: 971dfd82c4ba65baec923ad6a536725c1a80f472452811edcc17c3436ba256c3
Stable URL of this page: https://metraipolis.com/documento/dc_9c2ed4476a67

How to cite

Bounds on the Posterior-to-Prior Ratios for Inclusion Belief under Bounded Differential Privacy — arXiv:2608.30473 — arXiv (en), https://arxiv.org/abs/2608.30473 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9c2ed4476a67 (Metraipolis archive dc_9c2ed4476a67, sha256 971dfd82c4ba65baec923ad6a536725c1a80f472452811edcc17c3436ba256c3)

BibTeX

@misc{dc9c2ed4476a67,
  title = {Bounds on the Posterior-to-Prior Ratios for Inclusion Belief under Bounded Differential Privacy — arXiv:2608.30473},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.30473},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9c2ed4476a67; sha256 971dfd82c4ba65baec923ad6a536725c1a80f472452811edcc17c3436ba256c3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.30473. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Differential privacy has become the standard for generating privacy-protected data releases. However, differential privacy does not translate intuitively to disclosure risk. In particular, it remains unclear how much an adversary's belief about an individual's inclusion in a dataset can change after observing a protected release. To address this question, we derive upper and lower bounds on the posterior-to-prior ratios of inclusion beliefs under bounded probabilistic and approximate differential privacy. By assuming a worst-case adversary with all-but-one auxiliary information, i.e., knowledge of all except for one of the participants in a dataset, we obtain bounds that apply to any adversary. Because these bounds may fail with non-zero probability, we study the corresponding failure probability for the Gaussian mechanism. We derive a theoretical upper limit on this probability and compare it with Monte Carlo estimates across a wide range of parameter settings. The observed failure rate is several orders of magnitude smaller than its theoretical upper limit, indicating that the latter is highly conservative. These findings suggest that the inferential privacy guarantees provided by differentially private mechanisms may be substantially stronger in practice than what is implied by the theoretical upper limit.

Tema degli esploratori: fiducia digitale e crittografia (retro-catalogo arXiv: annunci del 2026-09-01 in cs.CR).
Categorie arXiv: Statistics Theory (math.ST) ; Cryptography and Security (cs.CR).
Pagina del lavoro: https://arxiv.org/abs/2608.30473 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:10:59.906Z dalla pagina https://arxiv.org/catchup/cs.CR/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).