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On Linear Refinement of Differential Privacy-Preserving Query Answering

机译：差分隐私保护查询应答的线性细化

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摘要

Recent work showed the necessity of incorporating a user's background knowledge to improve the accuracy of estimates from noisy responses of histogram queries. Various types of constraints (e.g., linear constraints, ordering constraints, and range constraints) may hold on the true (non-randomized) answers of histogram queries. So the idea was to apply the constraints over the noisy responses and find a new set of answers (called refinements) that are closest to the noisy responses and also satisfy known constraints. As a result, the refinements expect to boost the accuracy of final histogram query results. However, there is one key question: is the ratio of the distributions of the results after refinements from any two neighbor databases still bounded? In this paper, we introduce a new definition, ρ-differential privacy on refinement, to quantify the change of distributions of refinements. We focus on one representative refinement, the linear refinement with linear constraints and study the relationship between the classic e-differential privacy ( on responses) and our ρ-differential privacy on refinement. We demonstrate the conditions when the ρ-differential privacy on refinement achieves the same e-differential privacy. We argue privacy breaches could incur when the conditions do not meet.
机译：最近的工作表明，必须结合用户的背景知识，以提高直方图查询的嘈杂响应估计的准确性。各种类型的约束（例如，线性约束，排序约束和范围约束）可以保持直方图查询的真实（非随机）答案。因此，想法是将约束应用于噪声响应，并找到最接近噪声响应并满足已知约束的一组新答案（称为优化）。结果，这些改进有望提高最终直方图查询结果的准确性。但是，有一个关键问题：从任意两个相邻数据库进行细化后，结果的分布比例是否仍然有界？在本文中，我们引入了一个新的定义，即精炼中的ρ-差分隐私，以量化精炼分布的变化。我们专注于一种代表性的细化，即具有线性约束的线性细化，并研究经典电子差分隐私（在响应上）与我们的ρ微分隐私在细化之间的关系。我们证明了当精化的ρ-微分隐私获得相同的e-微分隐私时的条件。我们认为，如果条件不符合，可能会导致违反隐私的行为。

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