Robust and Private Bayesian Inference

@inproceedings{Dimitrakakis2014RobustAP,
  title={Robust and Private Bayesian Inference},
  author={Christos Dimitrakakis and Blaine Nelson and Aikaterini Mitrokotsa and Benjamin I. P. Rubinstein},
  booktitle={ALT},
  year={2014}
}
We examine the robustness and privacy of Bayesian inference, under assumptions on the prior, and with no modifications to the Bayesian framework. First, we generalise the concept of differential privacy to arbitrary dataset distances, outcome spaces and distribution families. We then prove bounds on the robustness of the posterior, introduce a posterior sampling mechanism, show that it is differentially private and provide finite sample bounds for distinguishability-based privacy under a strong… 

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