Perturb-and-Project: Differentially Private Similarities and Marginals

• URL: http://arxiv.org/abs/2406.04868v3
• Date: Wed, 7 Aug 2024 22:00:18 GMT
• Title: Perturb-and-Project: Differentially Private Similarities and Marginals
• Authors: Vincent Cohen-Addad, Tommaso d'Orsi, Alessandro Epasto, Vahab Mirrokni, Peilin Zhong,
• Abstract summary: We revisit the input perturbations framework for differential privacy where noise is added to the input $Ain mathcalS$. We first design novel efficient algorithms to privately release pair-wise cosine similarities. We derive a novel algorithm to compute $k$-way marginal queries over $n$ features.
• Score: 73.98880839337873
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We revisit the input perturbations framework for differential privacy where noise is added to the input $A\in \mathcal{S}$ and the result is then projected back to the space of admissible datasets $\mathcal{S}$. Through this framework, we first design novel efficient algorithms to privately release pair-wise cosine similarities. Second, we derive a novel algorithm to compute $k$-way marginal queries over $n$ features. Prior work could achieve comparable guarantees only for $k$ even. Furthermore, we extend our results to $t$-sparse datasets, where our efficient algorithms yields novel, stronger guarantees whenever $t\le n^{5/6}/\log n\,.$ Finally, we provide a theoretical perspective on why \textit{fast} input perturbation algorithms works well in practice. The key technical ingredients behind our results are tight sum-of-squares certificates upper bounding the Gaussian complexity of sets of solutions.

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