ABCDP: Approximate Bayesian Computation with Differential Privacy
This work addresses privacy concerns in Bayesian inference for data analysts, but it is incremental as it adapts an existing privacy technique to a specific computational method.
The authors tackled the problem of making approximate Bayesian computation (ABC) differentially private by developing ABCDP, which uses the Sparse Vector Technique to reduce cumulative privacy loss, resulting in posterior samples with high privacy levels while analyzing the trade-off between added noise and accuracy.
We develop a novel approximate Bayesian computation (ABC) framework, ABCDP, that produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the Sparse Vector Technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is met sparsely during the repeated queries, SVT can drastically reduces the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold, we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyze the interplay between the noise added for privacy and the accuracy of the posterior samples.