Canonical Noise Distributions and Private Hypothesis TestsDownload PDF

Published: 04 Nov 2021, Last Modified: 15 May 2023PRIML 2021 OralReaders: Everyone
Keywords: differential privacy, p-values, frequentist inference, optimal mechanism
TL;DR: "Canonical noise distribution" captures whether a mechanism fully uses the privacy budget, and leads to optimal private hypothesis tests.
Abstract: In the setting of $f$-DP, we propose the concept \emph{canonical noise distribution} (CND) which captures whether an additive privacy mechanism is tailored for a given $f$, and give a construction of a CND for an arbitrary tradeoff function $f$. We show that private hypothesis tests are intimately related to CNDs, allowing for the release of private $p$-values at no additional privacy cost as well as the construction of uniformly most powerful (UMP) tests for binary data. We apply our techniques to difference of proportions testing.
Paper Under Submission: The paper is NOT under submission at NeurIPS
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