Papers › Differentially Private Set Union

Differentially Private Set Union

22 Feb 2020ICML 2020 1arXiv:2002.09745archive 2025-07-28

Sivakanth Gopi, Pankaj Gulhane, Janardhan Kulkarni, Judy Hanwen Shen, Milad Shokouhi, Sergey Yekhanin

We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe U of items, possibly of infinite size, and a database D of users. Each user i contributes a subset Wᵢ ⊆U of items. We want an (ϵ,δ)-differentially private algorithm which outputs a subset S ⊂∪ᵢ Wᵢ such that the size of S is as large as possible. The problem arises in countless real world applications; it is particularly ubiquitous in natural language processing (NLP) applications as vocabulary extraction. For example, discovering words, sentences, n-grams etc., from private text data belonging to users is an instance of the set union problem. Known algorithms for this problem proceed by collecting a subset of items from each user, taking the union of such subsets, and disclosing the items whose noisy counts fall above a certain threshold. Crucially, in the above process, the contribution of each individual user is always independent of the items held by other users, resulting in a wasteful aggregation process, where some item counts happen to be way above the threshold. We deviate from the above paradigm by allowing users to contribute their items in a dependent fashion, guided by a policy. In this new setting ensuring privacy is significantly delicate. We prove that any policy which has certain contractive properties would result in a differentially private algorithm. We design two new algorithms, one using Laplace noise and other Gaussian noise, as specific instances of policies satisfying the contractive properties. Our experiments show that the new algorithms significantly outperform previously known mechanisms for the problem.

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