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arXiv 2009.11257stat.MEmath.STstat.TH
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基于信息论的差分隐私下事后随机化方法

An Information Theoretic approach to Post Randomization Methods under Differential Privacy

Fadhel Ayed, Marco Battiston, Federico Camerlenghi

摘要:

后随机化方法(PRAM)是分类和连续数据最流行的披露限制技术之一。在分类情况下,给定随机阵$M$和指定变量,属于类别$i$的个体以概率$M_{i,j}$变为类别$j$。选择随机化矩阵$M$的每种方法都必须在两个必要条件之间进行平衡:1)尽可能多地保留原始数据中的统计信息; 2)保证数据集中个体的隐私。这种权衡通常被证明是非常具有挑战性的解决。在这项工作中,我们使用最近的工具,从计算机科学文献,并建议选择$M$作为解决方案的约束最大化问题。具体来说,$M$被选为一个约束最大化问题的解决方案,在那里我们最大化的原始数据和转换后的数据之间的互信息,给定的约束,转换满足差分隐私的概念。对于一般的分类模型,它示出了这个最大化问题如何减少到一个凸线性规划,因此可以用已知的优化算法来解决。

英文摘要:

Post Randomization Methods (PRAM) are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix $M$ and a specified variable, an individual belonging to category $i$ is changed to category $j$ with probability $M_{i,j}$. Every approach to choose the randomization matrix $M$ has to balance between two desiderata: 1) preserving as much statistical information from the raw data as possible; 2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose $M$ as the solution of a constrained maximization problems. Specifically, $M$ is chosen as the solution of a constrained maximization problem, where we maximize the Mutual Information between raw and transformed data, given the constraint that the transformation satisfies the notion of Differential Privacy. For the general Categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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