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On the Differential Privacy of Bayesian Inference

Author

Listed:
  • Zuhe Zhang

    (University of Melbourne)

  • Benjamin Rubinstein

    (University of Melbourne)

  • Christos Dimitrakakis

    (SEQUEL - Sequential Learning - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 - Centrale Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique, Université de Lille, Sciences Humaines et Sociales, Chalmers University of Technology [Göteborg])

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.

Suggested Citation

  • Zuhe Zhang & Benjamin Rubinstein & Christos Dimitrakakis, 2016. "On the Differential Privacy of Bayesian Inference," Post-Print hal-01234215, HAL.
  • Handle: RePEc:hal:journl:hal-01234215
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01234215v2
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    Keywords

    Bayesian inference; posterior sampling; differential privacy;
    All these keywords.

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