ABCDP: Approximate Bayesian Computation with Differential Privacy

Abstract

We develop a novel approximate Bayesian computation (ABC) framework, ABCDP, that obeys the notion of differential privacy (DP). Under our framework, simply performing ABC inference with a mild modification yields differentially private posterior samples. We theoretically analyze the interplay between the ABC similarity threshold abc (for comparing the similarity between real and simulated data) and the resulting privacy level dp of the posterior samples, in two types of frequently-used ABC algorithms. We apply ABCDP to simulated data as well as privacysensitive real data. The results suggest that tuning the similarity threshold abc helps us obtain better privacy and accuracy trade-off.