Rényi Pufferfish Privacy with Gaussian-based Priors: From Single Gaussian to Mixture Model
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910167026630656 |
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| author | Yang, Wenjin Ding, Ni Zhang, Zijian Li, Zhen Sun, Jing An, Jincheng Liu, Yong Zhu, Liehuang |
| author_facet | Yang, Wenjin Ding, Ni Zhang, Zijian Li, Zhen Sun, Jing An, Jincheng Liu, Yong Zhu, Liehuang |
| contents | Rényi Pufferfish Privacy (RPP) provides a Rényi divergence-based privacy framework for correlated data, but existing $\infty$-Wasserstein mechanisms are often conservative and sacrifice data utility. We study Gaussian mechanisms for RPP under Gaussian and Gaussian-mixture priors. For single Gaussian priors, we derive the exact Rényi divergence after Gaussian perturbation, obtain a relaxed closed-form sufficient condition for $(α,ε)$-RPP, and characterize the monotonicity of the calibrated noise with respect to the privacy budget $ε$ and the Rényi order $α$. To handle more general non-Gaussian and multimodal priors, we approximate secret-conditioned outputs with Gaussian mixture models and introduce an optimal-transport-based sufficient condition for RPP. Experiments on three UCI datasets with statistical (\textsc{RAW}, \textsc{MEAN}) and model-output (\textsc{BNN}, \textsc{GP}) queries show that our prior-aware mechanisms consistently require less noise than a recent RPP additive-noise baseline, achieving an average noise reduction of 48.9\%. These results show that our mechanisms can substantially improve the privacy-utility trade-off under RPP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23649 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rényi Pufferfish Privacy with Gaussian-based Priors: From Single Gaussian to Mixture Model Yang, Wenjin Ding, Ni Zhang, Zijian Li, Zhen Sun, Jing An, Jincheng Liu, Yong Zhu, Liehuang Cryptography and Security Rényi Pufferfish Privacy (RPP) provides a Rényi divergence-based privacy framework for correlated data, but existing $\infty$-Wasserstein mechanisms are often conservative and sacrifice data utility. We study Gaussian mechanisms for RPP under Gaussian and Gaussian-mixture priors. For single Gaussian priors, we derive the exact Rényi divergence after Gaussian perturbation, obtain a relaxed closed-form sufficient condition for $(α,ε)$-RPP, and characterize the monotonicity of the calibrated noise with respect to the privacy budget $ε$ and the Rényi order $α$. To handle more general non-Gaussian and multimodal priors, we approximate secret-conditioned outputs with Gaussian mixture models and introduce an optimal-transport-based sufficient condition for RPP. Experiments on three UCI datasets with statistical (\textsc{RAW}, \textsc{MEAN}) and model-output (\textsc{BNN}, \textsc{GP}) queries show that our prior-aware mechanisms consistently require less noise than a recent RPP additive-noise baseline, achieving an average noise reduction of 48.9\%. These results show that our mechanisms can substantially improve the privacy-utility trade-off under RPP. |
| title | Rényi Pufferfish Privacy with Gaussian-based Priors: From Single Gaussian to Mixture Model |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2604.23649 |