Differentially Private H-Tree

In this paper, we study the problem of publishing a synopsis of two-dimensional datasets using differential privacy. The challenge is to enable accurate answers range count queries given a privacy budget. The state-of-the-art methods either construct a hierarchy of the partitions, or lay a one or two-level equi-width grid over the data domain, which are not suitable for high dimension and skewed datasets, respectively. To overcome such issues, we propose a technique that takes advantage of a two-level tree and a data-dependent method, namely private h-tree. As the height of the tree is kept low, h-tree requires less budget for node counts and thus more budget can be used for median splits. As splitting points of h-tree must be selected privately, we propose a recursive budget strategy to minimize noise added to the queries by reducing the number of median splits from linear to logarithmic. As a data-dependent approach, private h-tree provides accurate answers for range count queries under skewed data distribution. Experimental results on both real-world and synthetic datasets compare the accuracy of our proposed solution with the state-of-the-art methods, showing the superiority of our approach, particularly with skewed datasets in the presence of outliers.