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The iterative Bayesian update (IBU) and the matrix inversion (INV) are themain methods to retrieve the original distribution from noisy data resultingfrom the application of privacy protection mechanisms. We show that thetheoretical foundations of the IBU established in the literature are flawed, asthey rely on an assumption that in general is not satisfied in typical realdatasets. We then fix the theory of the IBU, by providing a general convergenceresult for the underlying Expectation-Maximization method. Our framework doesnot rely on the above assumption, and also covers a more general local privacymodel. Finally we evaluate the precision of the IBU on data sanitized with theGeometric, $k$-RR, and RAPPOR mechanisms, and we show that it outperforms INVin the first case, while it is comparable to INV in the other two cases.

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