Abstract

We investigate the natural connection between differential privacy and probabilistic inference, the former giving noisy observations about hidden data, and the latter telling us exactly what to do with these observations. As an example, we use the problem of logistic regression; we take a natural differentially-private heuristic (noisy gradient ascent) and show how the application of probabilistic inference allows for more accurate, and more concentrated conclusions. We go on to describe the design of a generic adaptation of the Privacy Integrated Queries allowing analysts without formal training in privacy or statistics to write algorithms and accurately interpret their results.