Differentially Private Set Union

By S. Gopi, P. Gulhane, Janardhan Kulkarni, Judy Hanwen Shen, Milad Shokouhi, Sergey Yekhanin. 2020

38 citations recorded by the source corpus.

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 $W_i \subseteq U$ of items. We want an ($\epsilon$,$\delta$)-differentially private algorithm which outputs a subset $S \subset \cup_i W_i$ 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 {\em dependent fashion}, guided by a {\em policy}. In this new setting ensuring privacy is significantly delicate. We prove that any policy which has certain {\em contractive} properties would result in a differentially private algorithm. We design two new algorithms for differentially private set union, one using Laplace noise and other Gaussian noise, which use $\ell_1$-contractive and $\ell_2$-contractive policies respectively and provide concrete examples of such policies. Our experiments show that the new algorithms in combination with our policies significantly outperform previously known mechanisms for the problem.

Subfields: Artificial Intelligence

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Citations in the corpus

Privacy in Deep Learning: A Survey (2020, methodology): “ uses a technique named RAPPOR [71] to allow web browser developers to privately collect usage statistics. A large body of Differentially private mechanisms has been proposed for various applications [73, 24, 74]. Triastcyn & Faltings present a technique that generates synthetic datasets that st”
Submix: Practical Private Prediction for Large-Scale Language Models (2022, background): “Other related works exploring privacy in natural language processing include (Gopi et al., 2020; Lyu et al., 2020; Xu et al., 2020; Li et al., 2018; Kim et al., 2021).”