ABCDP: Approximate Bayesian Computation Meets Differential Privacy
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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 ϵ_abc (for comparing the similarity between real and simulated data) and the resulting privacy level ϵ_dp of the posterior samples, in two types of frequently-used ABC algorithms. We apply ABCDP to simulated data as well as privacy-sensitive real data. The results suggest that tuning the similarity threshold ϵ_abc helps us obtain better privacy and accuracy trade-off.
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