Bayesian Decision-Theoretic Privacy

Overview

Recurrent data leaks and attacks on trained models are a reminder that the privacy of individuals in shared data cannot be taken for granted. Theoretical and applied research on privacy covers a very broad range of approaches and aims. This first lecture reviews the two reference formulations. The first approach is statistical disclosure control, as practiced by national statistical institutes. It covers re-identification risk, k-anonymity, recoding, perturbation, the cell key method and record swapping, illustrated on surveys and recent censuses. The second one is differential privacy, with Laplace and Gaussian randomization mechanisms as examples and justifications based on composition, hypothesis-testing and Bayesian interpretations. Its adoption for the 2020 US Census serves as an example. From a statistical perspective, both meet with limitations. Disclosure control relies on heuristics, gives no formal guarantee and cannot account for repeated releases and record linkage. Differential privacy is a worst-case property of the release mechanism, models no adversary, and leaves the choice of ε hard to interpret. A third route is to release only robust and deliberately insufficient statistics, such as a maximum likelihood estimator, an interquartile range, or a few quantiles. Such statistics are less sensitive to outliers and offer more protection through their higher breakdown point. Bayesian inference remains possible from these summaries, by simulating the unobserved data within a Gibbs sampler (Luciano, Robert & Ryder, 2024). How much privacy such deterministic releases provide is, however, beyond the reach of differential privacy.