Adaptive differentially private histogram of low-dimensional data

Abstract

We want to publish low-dimensional points, for example 2D spatial points, in a differentially private manner. Most existing mechanisms publish noisy frequency counts of points in a fixed predefined partition. Arguably, histograms with adaptive partition, for example V-optimal and equi-depth histograms, which have smaller bin-widths in denser regions, would provide more statistical information. However, as the adaptive partitions leak significant information about the dataset, it is not clear how differentially private partitions can be published accurately. In this paper, we propose a simple method based on the observation that the sensitivity of publishing the sorted sequence of a dataset is independent of the size of dataset. Together with isotonic regression, the dataset can be reconstructed with high accuracy. One advantage of the proposed method is its simplicity, in the sense that there are only a few parameters to be determined. Furthermore, the parameters can be estimated solely from the privacy requirement ε and the total number of points, and hence do not leak information about the data. Although the parameters are chosen to minimize the earth mover's distance between the published data and original data, empirical studies show that the proposed method also achieves high accuracy w.r.t. to some other measurements, for example range query and order statistics. © Springer-Verlag Berlin Heidelberg 2012.