Private selection from private candidates

Liu, Jingcheng; Talwar, Kunal

doi:10.1145/3313276.3316377

Cited by 51 publications

(56 citation statements)

References 31 publications

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“…3) finally, one could also run all the algorithms in parallel and choose the best performing one. Here we will have to account for the loss in privacy budget; see Liu and Talwar [2019] for example.…”

Section: Methodsmentioning

confidence: 99%

Differentially Private Set Union

Gopi

Gulhane

Kulkarni

et al. 2021

JPC

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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.

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Section: Methodsmentioning

confidence: 99%

Differentially Private Set Union

Gopi

Gulhane

Kulkarni

et al. 2021

JPC

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“…Other proposed mechanisms for private selection are the large margin mechanism that guarantees approximate differential privacy [26], or the more scalable subsampled exponential mechanism [27]. Other studies propose considering the quality functions themselves differentially private for cases where one cannot use the exponential mechanism [28], or a generalization of the exponential mechanism to handle quality functions of varying sensitivity [29]. In contrast, while our new mechanism also tackles differentially private selection, it is unique in the use of RR to increase the accuracy of the output.…”

Section: Differential Privacy Selectionmentioning

confidence: 99%

Exponential Randomized Response: Boosting Utility in Differentially Private Selection

Garrido¹,

Matthes²

2022

Preprint

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A differentially private selection algorithm outputs from a finite set the item that approximately maximizes a datadependent quality function. The most widely adopted mechanisms tackling this task are the pioneering exponential mechanism and permute-and-flip, which can offer utility improvements of up to a factor of two over the exponential mechanism. This work introduces a new differentially private mechanism for private selection and conducts theoretical and empirical comparisons with the above mechanisms. For reasonably common scenarios, our mechanism can provide utility improvements of factors significantly larger than two over the exponential and permute-and-flip mechanisms. Because the utility can deteriorate in niche scenarios, we recommend our mechanism to analysts who can tolerate lower utility for some datasets.

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“…31 The number of mixture components K was set to 10 for data with fewer dimensions (<20) and to 20 for data with more dimensions (R20). If necessary, this number, along with hyperparameters of DPVI, could be optimized under DP 32 , with potentially significant extra computational cost.…”

Section: Mixture Modelmentioning

confidence: 99%