On the Privacy of Selection Mechanisms with Gaussian Noise
CoRR(2024)
摘要
Report Noisy Max and Above Threshold are two classical differentially private
(DP) selection mechanisms. Their output is obtained by adding noise to a
sequence of low-sensitivity queries and reporting the identity of the query
whose (noisy) answer satisfies a certain condition. Pure DP guarantees for
these mechanisms are easy to obtain when Laplace noise is added to the queries.
On the other hand, when instantiated using Gaussian noise, standard analyses
only yield approximate DP guarantees despite the fact that the outputs of these
mechanisms lie in a discrete space. In this work, we revisit the analysis of
Report Noisy Max and Above Threshold with Gaussian noise and show that, under
the additional assumption that the underlying queries are bounded, it is
possible to provide pure ex-ante DP bounds for Report Noisy Max and pure
ex-post DP bounds for Above Threshold. The resulting bounds are tight and
depend on closed-form expressions that can be numerically evaluated using
standard methods. Empirically we find these lead to tighter privacy accounting
in the high privacy, low data regime. Further, we propose a simple privacy
filter for composing pure ex-post DP guarantees, and use it to derive a fully
adaptive Gaussian Sparse Vector Technique mechanism. Finally, we provide
experiments on mobility and energy consumption datasets demonstrating that our
Sparse Vector Technique is practically competitive with previous approaches and
requires less hyper-parameter tuning.
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