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Article

ABCDP: Approximate Bayesian Computation with Differential Privacy

1
Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
2
Max Planck Institute for Intelligent Systems, 72076 Tübingen, Germany
3
Department of Computer Science, University of Tübingen, 72076 Tübingen, Germany
4
Google Research, 80636 Munich, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Pierre Alquier
Entropy 2021, 23(8), 961; https://doi.org/10.3390/e23080961
Received: 19 May 2021 / Revised: 15 July 2021 / Accepted: 20 July 2021 / Published: 27 July 2021
(This article belongs to the Special Issue Approximate Bayesian Inference)
We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which 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 sparsely met during the repeated queries, SVT can drastically reduce 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 can 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 analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework. View Full-Text
Keywords: approximate Bayesian computation (ABC); differential privacy (DP); sparse vector technique (SVT) approximate Bayesian computation (ABC); differential privacy (DP); sparse vector technique (SVT)
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MDPI and ACS Style

Park, M.; Vinaroz, M.; Jitkrittum, W. ABCDP: Approximate Bayesian Computation with Differential Privacy. Entropy 2021, 23, 961. https://doi.org/10.3390/e23080961

AMA Style

Park M, Vinaroz M, Jitkrittum W. ABCDP: Approximate Bayesian Computation with Differential Privacy. Entropy. 2021; 23(8):961. https://doi.org/10.3390/e23080961

Chicago/Turabian Style

Park, Mijung, Margarita Vinaroz, and Wittawat Jitkrittum. 2021. "ABCDP: Approximate Bayesian Computation with Differential Privacy" Entropy 23, no. 8: 961. https://doi.org/10.3390/e23080961

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