Mean estimation over numeric data with personalized local differential privacy

The fast development of the Internet and mobile devices results in a crowdsensing business model, where individuals (users) are willing to contribute their data to help the institution (data collector) analyze and release useful information. However, the reveal of personal data will bring huge privacy threats to users, which will impede the wide application of the crowdsensing model. To settle the problem, the definition of local differential privacy (LDP) is proposed. Afterwards, to respond to the varied privacy preference of users, researchers propose a new model, i.e., personalized local differential privacy (PLDP), which allow users to specify their own privacy parameters. In this paper, we focus on a basic task of calculating the mean value over a single numeric attribute with PLDP. Based on the previous schemes for mean estimation under LDP, we employ PLDP model to design novel schemes (LAP, DCP, PWP) to provide personalized privacy for each user. We then theoretically analysis the worst-case variance of three proposed schemes and conduct experiments on synthetic and real datasets to evaluate the performance of three methods. The theoretical and experimental results show the optimality of PWP in the low privacy regime and a slight advantage of DCP in the high privacy regime.