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Full Convergence of the Iterative Bayesian Update and Applications to Mechanisms for Privacy Protection

Ehab Elsalamouny 1 Catuscia Palamidessi 2
2 COMETE - Concurrency, Mobility and Transactions
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : The iterative Bayesian update (IBU) and the matrix inversion (INV) are the main methods to retrieve the original distribution from noisy data resulting from the application of privacy protection mechanisms. We show that the theoretical foundations of the IBU established in the literature are flawed, as they rely on an assumption that in general is not satisfied in typical real datasets. We then fix the theory of the IBU, by providing a general convergence result for the underlying Expectation-Maximization method. Our framework does not rely on the above assumption, and also covers a more general local privacy model. Finally we evaluate the precision of the IBU on data sanitized with the Geometric, $k$-RR, and RAPPOR mechanisms, and we show that it outperforms INV in the first case, while it is comparable to INV in the other two cases.
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https://hal.inria.fr/hal-03091504
Contributor : Catuscia Palamidessi <>
Submitted on : Thursday, December 31, 2020 - 10:04:37 AM
Last modification on : Monday, January 11, 2021 - 2:25:56 PM

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  • HAL Id : hal-03091504, version 1
  • ARXIV : 1909.02961

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Ehab Elsalamouny, Catuscia Palamidessi. Full Convergence of the Iterative Bayesian Update and Applications to Mechanisms for Privacy Protection. EuroS&P 2020 - 5th IEEE European Symposium on Security and Privacy, Sep 2020, Genova, Italy. pp.490-507. ⟨hal-03091504⟩

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