Computer Science > Cryptography and Security
[Submitted on 3 Apr 2022 (v1), last revised 14 Dec 2022 (this version, v3)]
Title:Formal Privacy for Partially Private Data
View PDFAbstract:Differential privacy (DP) quantifies privacy loss by analyzing noise injected into output statistics. For non-trivial statistics, this noise is necessary to ensure finite privacy loss. However, data curators frequently release collections of statistics where some use DP mechanisms and others are released as-is, i.e., without additional randomized noise. Consequently, DP alone cannot characterize the privacy loss attributable to the entire collection of releases. In this paper, we present a privacy formalism, $(\epsilon, \{ \Theta_z\}_{z \in \mathcal{Z}})$-Pufferfish ($\epsilon$-TP for short when $\{ \Theta_z\}_{z \in \mathcal{Z}}$ is implied), a collection of Pufferfish mechanisms indexed by realizations of a random variable $Z$ representing public information not protected with DP noise. First, we prove that this definition has similar properties to DP. Next, we introduce mechanisms for releasing partially private data (PPD) satisfying $\epsilon$-TP and prove their desirable properties. We provide algorithms for sampling from the posterior of a parameter given PPD. We then compare this inference approach to the alternative where noisy statistics are deterministically combined with Z. We derive mild conditions under which using our algorithms offers both theoretical and computational improvements over this more common approach. Finally, we demonstrate all the effects above on a case study on COVID-19 data.
Submission history
From: Jeremy Seeman [view email][v1] Sun, 3 Apr 2022 16:13:58 UTC (2,811 KB)
[v2] Thu, 26 May 2022 23:32:36 UTC (694 KB)
[v3] Wed, 14 Dec 2022 17:03:18 UTC (759 KB)
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