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arXiv · 2406.04868

Perturb-and-Project: Differentially Private Similarities and Marginals

Vincent Cohen-Addad·Tommaso d'Orsi·Alessandro Epasto·Vahab Mirrokni·Peilin Zhong
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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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Vincent Cohen-Addad, Tommaso d'Orsi, Alessandro Epasto, Vahab Mirrokni, Peilin Zhong. 2024-06-07. Perturb-and-Project: Differentially Private Similarities and Marginals. https://arxiv.org/abs/2406.04868

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