Efficient Discrete Distribution Estimation Schemes Under Local Differential Privacy

Abstract

AbstractRecently, local differential privacy (LDP) has increasingly been leveraged to cope with privacy issues in data collection. Discrete distribution estimation schemes under LDP are the fundamental tools in the LDP setting, which enable data collector to collect discrete distribution estimation information about a population while protecting each individual’s privacy, without relying on a trusted third party. Among these schemes, Ye-Barg mechanisms achieve the best utility in the medium privacy regime. Nevertheless, their communication cost between the user and data collector is O(k) which is too large to be deployed in practice when the domain size k is large (or even unbounded). In this paper, we propose a family of new efficient discrete distribution estimation schemes under LDP which reduce the communication cost to less than \(O(\mathrm {log}(2+e^\epsilon ))\) and obtain almost the same expected estimation loss as Ye-Barg mechanisms under \(\ell _2^2\) metric and \(\ell _1\) metric. Additionally, we compare our schemes with Ye-Barg mechanisms theoretically and experimentally and confirm our conclusion.KeywordsLocal differential privacyDiscrete distribution estimationUtilityCommunication cost