Full Convergence of the Iterative Bayesian Update and Applications to Mechanisms for Privacy Protection
This addresses reliability issues in privacy protection mechanisms for data analysts, though it is an incremental theoretical correction.
The paper identifies flawed theoretical foundations in the iterative Bayesian update (IBU) method for retrieving original distributions from privacy-protected data, fixes the theory with a general convergence result, and shows IBU outperforms matrix inversion for Geometric mechanisms while being comparable for k-RR and RAPPOR mechanisms.
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.