On the Differential Privacy of Bayesian Inference

Zuhe Zhang 1, * Benjamin Rubinstein 1 Christos Dimitrakakis 2, 3, 4
* Corresponding author
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian networks; and we introduce a maximum-a-posteriori private mechanism. Our analysis includes utility and privacy bounds, with a novel focus on the influence of graph structure on privacy. Worked examples and experiments with Bayesian naïve Bayes and Bayesian linear regression illustrate the application of our mechanisms.
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https://hal.inria.fr/hal-01234215
Contributor : Christos Dimitrakakis <>
Submitted on : Monday, December 21, 2015 - 8:42:02 PM
Last modification on : Thursday, March 21, 2019 - 2:50:30 PM
Long-term archiving on: Saturday, April 29, 2017 - 2:14:10 AM

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  • HAL Id : hal-01234215, version 1
  • ARXIV : 1512.06992

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Zuhe Zhang, Benjamin Rubinstein, Christos Dimitrakakis. On the Differential Privacy of Bayesian Inference. AAAI 2016, Feb 2016, Phoenix, Arizona, United States. ⟨hal-01234215v1⟩

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