Histogram Publishing Algorithm Based on Sampling Sorting and Greedy Clustering. The data produced by differential privacy histogram publishing algorithm based on grouping has low usability due to large approximation error and Laplace error. To solve this problem, a histogram publishing algorithm based on roulette sampling sort and greedy partition is proposed. Our algorithm combines the exponential mechanism with the roulette sampling sorting method, arranges the similar histogram bins together with a larger probability by the utility function and the restriction on the number of sampled entity. The greedy clustering algorithm is used to partition the sorted histogram bins into groups, and the error among histogram bins in each group is reduced by optimizing the lower bound error of the grouping. Extensive experimental results show that the proposed algorithm can effectively improve the usability of published data under the premise of satisfying differential privacy.

Collecting and Analyzing Multidimensional Data with Local Differential Privacy. Local differential privacy (LDP) is a recently proposed privacy standard for collecting and analyzing data, which has been used, e.g., in the Chrome browser, iOS and macOS. In LDP, each user perturbs her information locally, and only sends the randomized version to an aggregator who performs analyses, which protects both the users and the aggregator against private information leaks. Although LDP has attracted much research attention in recent years, the majority of existing work focuses on applying LDP to complex data andor analysis tasks. In this paper, we point out that the fundamental problem of collecting multidimensional data under LDP has not been addressed sufficiently, and there remains much room for improvement even for basic tasks such as computing the mean value over a single numeric attribute under LDP. Motivated by this, we first propose novel LDP mechanisms for collecting a numeric attribute, whose accuracy is at least no worse (and usually better) than existing solutions in terms of worstcase noise variance. Then, we extend these mechanisms to multidimensional data that can contain both numeric and categorical attributes, where our mechanisms always outperform existing solutions regarding worstcase noise variance. As a case study, we apply our solutions to build an LDPcompliant stochastic gradient descent algorithm (SGD), which powers many important machine learning tasks. Experiments using real datasets confirm the effectiveness of our methods, and their advantages over existing solutions.