On the Differential Privacy of Bayesian Inference

Zuhe Zhang (), Benjamin Rubinstein () and Christos Dimitrakakis
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Zuhe Zhang: University of Melbourne
Benjamin Rubinstein: University of Melbourne

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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.

Keywords: Bayesian inference; posterior sampling; differential privacy (search for similar items in EconPapers)
Date: 2016-02-10
New Economics Papers: this item is included in nep-ecm and nep-upt
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Published in AAAI 2016 - Thirtieth AAAI Conference on Artificial Intelligence, Feb 2016, Phoenix, Arizona, United States

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