用保序回归方法私下发布位置数据集差分
Publishing Location Dataset Differential Privately with Isotonic Regression
摘要：
我们考虑的问题，发布位置数据集，特别是2D空间点集，在一个不同的私人方式。许多现有的机制集中在一些先验分区的域，这是很难确定的点的频率计数。我们提出了一种方法，直接添加噪声的点，或一组相邻的点。我们的方法是基于这样的观察，排序的灵敏度，作为一个功能的实数集，可以有界。与保序回归一起，可以准确地重建数据集。为了将该机制扩展到更高的维度，我们使用局部保持函数将数据集映射到一个有界区间。虽然局部保持函数的性能存在根本限制，但幸运的是，我们的问题只需要在“更容易”的方向上保持距离，并且众所周知的希尔伯特空间填充曲线足以提供高精度。从发布者的角度来看，发布过程很简单：发布者只需要映射数据，排序，分组，添加拉普拉斯噪声并发布数据集。要确定的唯一参数是可以基于预测的泛化误差来选择的组大小。实验结果表明，该方法还可以准确地回答其他查询，如范围查询和中位数查询。
英文摘要：
We consider the problem of publishing location datasets, in particular 2D spatial pointsets, in a differentially private manner. Many existing mechanisms focus on frequency counts of the points in some a priori partition of the domain that is difficult to determine. We propose an approach that adds noise directly to the point, or to a group of neighboring points. Our approach is based on the observation that, the sensitivity of sorting, as a function on sets of real numbers, can be bounded. Together with isotonic regression, the dataset can be accurately reconstructed. To extend the mechanism to higher dimension, we employ locality preserving function to map the dataset to a bounded interval. Although there are fundamental limits on the performance of locality preserving functions, fortunately, our problem only requires distance preservation in the "easier" direction, and the well-known Hilbert space-filling curve suffices to provide high accuracy. The publishing process is simple from the publisher's point of view: the publisher just needs to map the data, sort them, group them, add Laplace noise and publish the dataset. The only parameter to determine is the group size which can be chosen based on predicted generalization errors. Empirical study shows that the published dataset can also exploited to answer other queries, for example, range query and median query, accurately.
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