Accurate Histogram Release under Differential Privacy

Grouping-based differentially private histogram release has attracted considerable research attention in recent years. The trade-off between approximation error caused by the group’s mean and Laplace error due to Laplace noise constrains the accuracy of histogram release. Most existing methods based on grouping strategy cannot efficiently accommodate the both errors. This paper proposes an efficient differentially private method, called DiffHR (differentially private histogram release) to publish histograms. In order to boost the accuracy of the released histogram, DiffHR employs Metropolis-Hastings method in MCMC (Markov chain Monte Carlo) and the exponential mechanism to propose an efficient sorting method. This method generates a differentially private histogram by sampling and exchanging two buckets to approximate the correct order. To balance Laplace error and approximation error efficiently, a utility-driven adaptive clustering method is proposed in DiffHR to partition the sorted histogram. Furthermore, the time complexity of the clustering method is O(n). DiffHR is compared with existing methods such as GS, AHP on the real datasets. The experimental results show that DiffHR outperforms its competitors, and achieves the accurate results.