Kantorovich Mechanism for Pufferfish Privacy

Ni Ding
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:5084-5103, 2022.

Abstract

Pufferfish privacy achieves $\epsilon$-indistinguishability over a set of secret pairs in the disclosed data. This paper studies how to attain $\epsilon$-pufferfish privacy by exponential mechanism, an additive noise scheme that generalizes the Laplace noise. It is shown that the disclosed data is $\epsilon$-pufferfish private if the noise is calibrated to the sensitivity of the Kantorovich optimal transport plan. Such a plan can be obtained directly from the data statistics conditioned on the secret, the prior knowledge of the system. The sufficient condition is further relaxed to reduce the noise power. It is also proved that the Gaussian mechanism based on the Kantorovich approach attains the $\delta$-approximation of $\epsilon$-pufferfish privacy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ding22b, title = { Kantorovich Mechanism for Pufferfish Privacy }, author = {Ding, Ni}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {5084--5103}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/ding22b/ding22b.pdf}, url = {https://proceedings.mlr.press/v151/ding22b.html}, abstract = { Pufferfish privacy achieves $\epsilon$-indistinguishability over a set of secret pairs in the disclosed data. This paper studies how to attain $\epsilon$-pufferfish privacy by exponential mechanism, an additive noise scheme that generalizes the Laplace noise. It is shown that the disclosed data is $\epsilon$-pufferfish private if the noise is calibrated to the sensitivity of the Kantorovich optimal transport plan. Such a plan can be obtained directly from the data statistics conditioned on the secret, the prior knowledge of the system. The sufficient condition is further relaxed to reduce the noise power. It is also proved that the Gaussian mechanism based on the Kantorovich approach attains the $\delta$-approximation of $\epsilon$-pufferfish privacy. } }
Endnote
%0 Conference Paper %T Kantorovich Mechanism for Pufferfish Privacy %A Ni Ding %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-ding22b %I PMLR %P 5084--5103 %U https://proceedings.mlr.press/v151/ding22b.html %V 151 %X Pufferfish privacy achieves $\epsilon$-indistinguishability over a set of secret pairs in the disclosed data. This paper studies how to attain $\epsilon$-pufferfish privacy by exponential mechanism, an additive noise scheme that generalizes the Laplace noise. It is shown that the disclosed data is $\epsilon$-pufferfish private if the noise is calibrated to the sensitivity of the Kantorovich optimal transport plan. Such a plan can be obtained directly from the data statistics conditioned on the secret, the prior knowledge of the system. The sufficient condition is further relaxed to reduce the noise power. It is also proved that the Gaussian mechanism based on the Kantorovich approach attains the $\delta$-approximation of $\epsilon$-pufferfish privacy.
APA
Ding, N.. (2022). Kantorovich Mechanism for Pufferfish Privacy . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:5084-5103 Available from https://proceedings.mlr.press/v151/ding22b.html.

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