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Differential Privacy for Bayesian Inference through Posterior Sampling.
Journal
Journal of Machine Learning Research
ISSN
1532-4435
Type
journal article
Date Issued
2017
Author(s)
Abstract
Differential privacy formalises privacy-preserving mechanisms that provide access to a database. Can Bayesian inference be used directly to provide private access to data? The answer is yes: under certain conditions on the prior, sampling from the posterior distribution can lead to a desired level of privacy and utility. For a uniform treatment, we define differential privacy over arbitrary data set metrics, outcome spaces and distribution families. This allows us to also deal with non-i.i.d or non-tabular data sets. We then prove bounds on the sensitivity of the posterior to the data, which delivers a measure of robustness. We also show how to use posterior sampling to provide differentially private responses to queries, within a decision-theoretic framework. Finally, we provide bounds on the utility of answers to queries and on the ability of an adversary to distinguish between data sets. The latter are complemented by a novel use of Le Cam's method to obtain lower bounds on distinguishability. Our results hold for arbitrary metrics, including those for the common definition of differential privacy. For specific choices of the metric, we give a number of examples satisfying our assumptions.
Language
English
Keywords
Bayesian inference
differential privacy
robustness
adversarial Learning
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
Microtome Publishing
Volume
18
Number
11
Start page
1
End page
39
Pages
39
Subject(s)
Division(s)
Eprints ID
262929
File(s)